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Characterizing the Solution Set for Nonconvex Semi-Infinite Programs Involving Tangential Subdifferentials Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-22 Xian-Jun Long; Juan Liu; Nan-Jing Huang
Abstract The purpose of this paper is to study the characterization of the solution set for nonconvex semi-infinite programming problems related to tangential subdifferentials. We give a necessary optimality condition for the solution set of the nonconvex semi-infinite programming problem. We also prove that the Lagrangian function associated with a fixed Lagrange multiplier is constant on the solution
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High Order Fixed Point and Newton’s Methods in Banach Space Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-22 François Dubeau
Abstract Through Taylor’s expansions and a thorough analysis of the necessary and sufficient conditions that will entail for fixed point and Newton’s iterative methods to be of higher order convergence in Banach space, we are able to present a unified way to make these methods faster. Numerical examples illustrate the theoretical results.
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Weighted Estimates of the Cayley Transform Method for Boundary Value Problems in a Banach Space Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-20 V. L. Makarov; N. V. Mayko
Abstract We consider the boundary value problems (BVPs) for linear second-order ODEs with a strongly positive operator coefficient in a Banach space. The solutions are given in the form of the infinite series by means of the Cayley transform of the operator, the Meixner type polynomials of the independent variable, the operator Green function, and the Fourier series representation for the right-hand
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Special Issue Research on Generalized Inverses in China Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-12-24 M. Z. Nashed
(2020). Special Issue Research on Generalized Inverses in China. Numerical Functional Analysis and Optimization: Vol. 41, RESEARCH ON GENERALIZED INVERSES IN CHINA, pp. 1667-1668.
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Special Issue Research on Generalized Inverses in China Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-12-11 Yuwen Wang; Yimin Wei
(2020). Special Issue Research on Generalized Inverses in China. Numerical Functional Analysis and Optimization: Vol. 41, RESEARCH ON GENERALIZED INVERSES IN CHINA, pp. 1669-1671.
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Applications of Generalized Weighted Statistical Convergence to Approximation Theorems for Functions of One and Two Variables Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-16 Faruk Özger
Abstract In this article, we apply weighted A − statistical convergence to obtain some general approximation results for λ − Bernstein operators. We prove a weighted A − statistical Voronovskaja-type approximation theorem. We support our theoretical parts about approximation properties of constructed bivariate λ − Bernstein operators with numerical results and graphics.
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On the Convergence Rate of Spectral Approximations for the Equations of Nonhomogeneous Incompressible Fluids Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-16 E. Ortega-Torres; M. Poblete-Cantellano; M. A. Rojas-Medar
Abstract In this paper, we are concerned about the convergence rates of spectral semi-Galerkin methods to solve the equations describing the motion of a nonhomogeneous viscous incompressible fluid. This approach allows the study of density dependent viscosity.
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Making and Sharing K-Dual Frame Pairs Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-12 Ya-Nan Li; Yun-Zhang Li
Abstract The atomic decomposition of signals is one of the most important problems in the frame theory. K-dual frame pairs may be used to stably reconstruct elements from the range of bounded linear operators on Hilbert spaces. The purpose of this paper is making K-dual frame pairs and finding common K-dual Bessel sequence. We present a sufficient condition on operators on H which takes a K-dual frame
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Solving Optimization Problems over the Weakly Efficient Set Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-12 Javad Sadeghi; Hossein Mohebi
Abstract In this paper, we study the optimization problem (PWE) of minimizing a convex function over the set of weakly efficient solutions of a convex multiobjective problem. This is done by using the fact that each lower semicontinuous convex function is an upper envelope of its affine minorants together with a generalized cutting plane method. We give necessary conditions for optimal solutions of
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Sequence Convergence of Inexact Nonconvex and Nonsmooth Algorithms with More Realistic Assumptions Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-12 Tao Sun
Abstract The sequence convergence of inexact nonconvex and nonsmooth algorithms is proved with an unrealistic assumption on the noise. In this paper, we focus on removing the assumption. Without the assumption, the algorithm consequently cannot be proved with previous framework and tricks. Thus, we build a new proof framework which employs a pseudo sufficient descent condition and a pseudo relative
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Adaptive Approximation of Shapes Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-12 A. Buffa; R. Hiptmair; P. Panchal
Abstract We consider scalar-valued shape functionals on sets of shapes which are small perturbations of a reference shape. The shapes are described by parameterizations and their closeness is induced by a Hilbert space structure on the parameter domain. We justify a heuristic for finding the best low-dimensional parameter subspace with respect to uniformly approximating a given shape functional. We
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Dirichlet Theorem for Jacobi-Dunkl Expansions Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-11 Frej Chouchene; Iness Haouala
Abstract The purpose of this paper is to study the pointwise convergence of the Jacobi-Dunkl series. We establish a Dirichlet type theorem for expansions in term of Jacobi-Dunkl polynomials.
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Quasi-Inertial Tseng’s Extragradient Algorithms for Pseudomonotone Variational Inequalities and Fixed Point Problems of Quasi-Nonexpansive Operators Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-08 Tu-Yan Zhao; Dan-Qiong Wang; Lu-Chuan Ceng; Long He; Chun-Yan Wang; Hong-Ling Fan
Abstract In a real Hilbert space, let the VIP indicate a variational inequality problem with Lipschitzian, pseudomonotone operator, and let the FPP denote a fixed-point problem of a quasi-nonexpansive operator with a demiclosedness property. This article designs two quasi-inertial Tseng’s extragradient algorithms with adaptive stepsizes for finding a common solution of the VIP and FPP. The proposed
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A Dynamical Approach to Two-Block Separable Convex Optimization Problems with Linear Constraints Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2021-01-01 Sandy Bitterlich; Ernö Robert Csetnek; Gert Wanka
Abstract The aim of this manuscript is to approach by means of first order differential equations/inclusions convex programming problems with two-block separable linear constraints and objectives, whereby (at least) one of the components of the latter is assumed to be strongly convex. Each block of the objective contains a further smooth convex function. We investigate the dynamical system proposed
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Efficient Evaluation of Noncommutative Polynomials Using Tensor and Noncommutative Waring Decompositions Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-12-27 Eric Evert; J. William Helton; Shiyuan Huang; Jiawang Nie
Abstract This paper analyses a Waring type decomposition of a noncommuting (NC) polynomial p with respect to the goal of evaluating p efficiently on tuples of matrices. Such a decomposition can reduce the number of matrix multiplications needed to evaluate a noncommutative polynomial and is valuable when a single polynomial must be evaluated on many matrix tuples. In pursuit of this goal we examine
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Existence of Best Proximity Pairs and a Generalization of Carathéodory Theorem Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-12-22 Abhik Digar; G. Sankara Raju Kosuru
Abstract A new class of mappings, called relatively continuous, is introduced and incorporated to elicit best proximity pair theorems for a non-self-mapping in the setting of reflexive Banach space. As a consequence we obtain a generalization of Carathéodory extension theorem for an initial value problem with L 1 functions on the right hand side.
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Special Issue Research on Generalized Inverses in China Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-12-11 Yuwen Wang; Yimin Wei
(2020). Special Issue Research on Generalized Inverses in China. Numerical Functional Analysis and Optimization. Ahead of Print.
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Ill-Posed Nonlinear Optimization Problems and Uniform Accuracy Estimates of Regularization Methods Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-11-24 M. Yu. Kokurin
Abstract We investigate the ill-posed problem of minimizing weakly lower semicontinuous functionals on a convex closed set in a Hilbert space. The functionals to be minimized are available with errors. We prove that a necessary condition for the existence of a regularization procedure with a uniform accuracy estimate on the class of weakly lower semicontinuous functionals is the well-posedness of related
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Steklov Expansion Method for Regularized Harmonic Boundary Value Problems Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-11-16 Manki Cho
Abstract A new type of meshless method is proposed in this paper to solve regularized Laplacian boundary value problems of the form L u : = r 2 u − Δ u ≡ 0 . In this method, solving the Laplacian boundary value problem is starting from finding regularized Steklov eigenpairs which could provide the orthonormal basis of the space of solutions. The solutions are represented by orthogonal regularized Steklov
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A Decomposition Algorithm for the Sums of the Largest Eigenvalues Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-09 Ming Huang; Yue Lu; Jin Long Yuan; Yang Li
In this article, we consider optimization problems in which the sums of the largest eigenvalues of symmetric matrices are involved. Considered as functions of a symmetric matrix, the eigenvalues are not smooth once the multiplicity of the function is not single; this brings some difficulties to solve. For this, the function of the sums of the largest eigenvalues with affine matrix-valued mappings is
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The Multidimensional Damped Wave Equation: Maximal Weak Solutions for Nonlinear Forcing via Semigroups and Approximation Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-08 Joseph W. Jerome
The damped nonlinear wave equation, also known as the nonlinear telegraph equation, is studied within the framework of semigroups and eigenfunction approximation. The linear semigroup assumes a central role: it is bounded on the domain of its generator for all time t ≥ 0 . This permits eigenfunction approximation within the semigroup framework, as a tool for the study of weak solutions. The semigroup
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Sequential Evaluation Convergence of Operator Series and Its Application Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-02 Hongli Liu; Guanqi Liu
Abstract For a class of classical vector-valued sequence spaces in Banach spaces, this article introduces a class of important subsets, which contain all the fully bounded sets and many non-bounded sets in the sequence spaces. Using this collection class, we obtain a convergence theorem for the assignment of series of operator series, and apply the conclusion to the characterization of infinite matrix
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BQL Generalized Inverse Condition for Multiple Transcritical and Pitchfork Bifurcation Theorem Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-02 Guanqi Liu; Yuwen Wang
Abstract In this article, by using the bounded quasi-linear projection generalized inverse, we prove the transcritical and pitchfork bifurcation theorem for multiple eigenvalues, which is a generalized result of the famous transcritical and pitchfork bifurcation theorem for simple eigenvalue.
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Shale Microstructure Prediction with Nonsmooth Sparse Regularizing X-Ray CT Imaging Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-02 Qinghua Ma; Zuoliang Xu; Yanfei Wang; Yu Wang; Lihua Wang; Jianqiang Wang
Abstract Microscopic analysis of mineral distributions in shale receives much attention in recent years. Traditional methods such as optical and scanning electron microscopy are common tools for providing valuable information of microstructures; however, they belong to surface observations, which damage the shale sample and only generate a 2D image. We consider using the X-ray computerized tomography
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Drazin Invertibility in a Certain Finite-Dimensional Algebra Generated by Two Idempotents Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-02 Jianlong Chen; Yuefeng Gao; Lifang Li
Abstract In this article, we study the existence criterion and formulae of Drazin inverses of elements in a certain finite-dimensional algebra generated by two idempotents, under some prescribed conditions.
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On the Stable Perturbation and Nashed’s Condition for Generalized Inverses† Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-02 Jiu Ding; Qianglian Huang
Abstract Let T be a bounded linear operator from a Banach space to a Banach space with closed range and let T¯=T+δT. Nashed’s condition is that (I+δTT+)−1T¯ maps the null space of T into the range of T. The stable perturbation means that the intersection of the range of T¯ and the null space of the generalized inverse of T is {0}. We show that the stable perturbation is the same as Nashed’s condition
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Perturbation Analysis for Oblique Projection Generalized Inverses Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-02 Fapeng Du; M. Zuhair Nashed
Abstract In this paper, we introduce the notion of stable perturbation of a subspace in Banach space. Utilizing this notion and the gap between subspaces, we develop a perturbation analysis for the oblique projection generalized inverse when the operator T, the range and null space of the projectors have perturbations simultaneously and estimate an upper bound of ||T¯P¯,Q¯+−TP,Q+||. Our results are
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Approximate Solutions of Impulsive Optimal Controls for a Class of Lagrange Problem Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-01 Lanping Zhu; Weiwei Pan; Gang Li
Abstract This work is devoted to establish the optimal solutions of impulsive optimal controls for a class of Lagrange problem. Using the approximate method and fixed point theorem, the corresponding semilinear system is solvable under some appropriate assumptions. From the derived results, we propose to construct two kinds of minimizing sequences of approximating solutions to obtain the optimal solutions
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Acute and Stable Perturbations of the Drazin Inverse of Bounded Linear Operators in Banach Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-01 Haifeng Ma
Abstract Let B (X) be the set of bounded linear operators on a Banach space X, and a liner operator A∈B (X) be Drazin invertible. A linear operator B∈B (X) is said to be a stable perturbation of A if B is Drazin invertible and I−Aπ−Bπ is invertible, where I is the identity operator on X, Aπ(=I−AAD) and Bπ(=I−BBD) are the spectral projectors of A and B respectively. We call B an acute perturbation of
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A Note on Perturbation Estimations for Spectral Projectors Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-09-01 Chuanning Song; Yimin Wei; Qingxiang Xu
Abstract For any singular matrix A∈Cn×n, let AD, Aπ=In−AAD be its Drazin inverse and spectral projector, respectively. Let ||·|| be any norm on Cn×n and A¯∈Cn×n be any stable perturbation of A. In this note a sufficient condition is given under which ||A¯π−Aπ||<1.
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Intertwining Operators between Two Orthogonal Projections Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-08-31 Chunyuan Deng; Wenting Liang
Abstract Let P and Q be a pair of orthogonal projections. In this note we will prove that there exists a unitary U∈B(H) such that UP = QU and UQ = PU if and only if dim[R(P)∩N(Q)]=dim[N(P)∩R(Q)].
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Estimating the Nonparametric Regression Function by Using Padé Approximation Based on Total Least Squares Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-08-20 Syed Ejaz Ahmed; Dursun Aydin; Ersin Yilmaz
In this paper, we propose a Padé-type approximation based on truncated total least squares (P – TTLS) and compare it with three commonly used smoothing methods: Penalized spline, Kernel smoothing and smoothing spline methods that have become very powerful smoothing techniques in the nonparametric regression setting. We consider the nonparametric regression model, y i = g ( x i ) + ε i , and discuss
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A One Dimensional Elliptic Distributed Optimal Control Problem with Pointwise Derivative Constraints Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-30 Susanne C. Brenner; Li-yeng Sung; Winnifried Wollner
We consider a one dimensional elliptic distributed optimal control problem with pointwise constraints on the derivative of the state. By exploiting the variational inequality satisfied by the derivative of the optimal state, we obtain higher regularity for the optimal state under appropriate assumptions on the data. We also solve the optimal control problem as a fourth order variational inequality
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On the Derivation of Quasi-Newton Formulas for Optimization in Function Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-07-13 Radoslav G. Vuchkov; Cosmin G. Petra; Noémi Petra
Newton’s method is usually preferred when solving optimization problems due to its superior convergence properties compared to gradient-based or derivative-free optimization algorithms. However, deriving and computing second-order derivatives needed by Newton’s method often is not trivial and, in some cases, not possible. In such cases quasi-Newton algorithms are a great alternative. In this paper
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Optimal Control of Time-Periodic Navier-Stokes-Voigt Equations Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-07-03 Cung The Anh; Tran Minh Nguyet
We consider a quadratic optimal control problem for the 3D Navier-Stokes-Voigt equations with periodic inputs. We prove the existence of optimal solutions, then establish necessary and sufficient optimality conditions. We also define semidiscrete-in-time approximations for the optimal control problem and then prove the existence of a subsequence that converges to an optimal solution.
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Analysis of Stabilized Crank-Nicolson Time-Stepping Scheme for the Evolutionary Peterlin Viscoelastic Model Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-07-08 S. S. Ravindran
The Peterlin viscoelastic model describes the motion of certain incompressible polymeric fluids. It employs a nonlinear dumbbell model with a nonlinear spring force law making it more nonlinear than other viscoelastic models. In this paper, we propose and study a fully implicit stabilized Crank-Nicolson time stepping scheme for finite element spatial discretization of the non-stationary Peterlin viscoelastic
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Density in L 2 ( Γ , μ ) of Certain Families of Functions on LCA Groups Related to the Multi-Channel Sampling Problem Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-08-12 Lutz P. Klotz; Juan M. Medina
Let G be an LCA group, H a closed subgroup, Γ the dual group of G and μ be a regular finite non-negative Borel measure on Γ. Motivated by the problem of sampling and reconstruction of a stationary random process over G from the values of m different linear measurements on H, we give some necessary or sufficient conditions for the density of certain sets of functions in L 2 ( Γ , μ ) , which arise in
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Optimal Control for Shape Memory Alloys of the One-Dimensional Frémond Model Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-12 Pierluigi Colli; M. Hassan Farshbaf-Shaker; Ken Shirakawa; Noriaki Yamazaki
In this article, we consider optimal control problems for the one-dimensional Frémond model for shape memory alloys. This model is constructed in terms of basic functionals like free energy and pseudo-potential of dissipation. The state problem is expressed by a system of partial differential equations involving the balance equations for energy and momentum. We prove the existence of an optimal control
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Weighted Composition Operators from the Zygmund Space to nth Weighted-Type Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-12 Ebrahim Abbasi; Songxiao Li
In this work, the boundedness and essential norm of weighted composition operators from the Zygmund space to nth weighted-type spaces are characterized. As a corollary, some characterizations for the compactness of weighted composition operators from the Zygmund space to nth weighted-type spaces are also presented.
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Numerical Verification of Solutions for Nonlinear Parabolic Problems Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-12 Kouji Hashimoto; Takehiko Kinoshita; Mitsuhiro T. Nakao
In this paper, we present a numerical verification method of solutions for nonlinear parabolic initial boundary value problems. Decomposing the problem into a nonlinear part and an initial value part, we apply Nakao’s projection method, which is based on the full-discrete finite element method with constructive error estimates, to the nonlinear part and use the theoretical analysis for the heat equation
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Iterated Boolean Sums of Bernstein Type Operators Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-10 Tuncer Acar; Ali Aral; Ioan Raşa
The approximation of functions using linear positive operators is affected by saturation. The quality of approximation offered by iterated Boolean sums increases with the regularity of the function. We present some qualitative and quantitative results concerning the approximation by such Boolean sums. The general results are illustrated by examples.
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Inexact Infinite Products of Weak Quasi-Contraction Mappings in b-Metric Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-22 Anuradha Gupta; Manu Rohilla
The influence of errors on the convergence of infinite products of weak quasi-contraction mappings in b-metric spaces is explored. An example demonstrating the necessity of convergence of the sequence of computational errors to zero is also provided. Moreover, we discuss weak ergodic theorems in the setting of b-metric spaces.
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Source Identification Problem for a Parabolic Equation with Multipoint Nonlocal Boundary Condition Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-08-06 Charyyar Ashyralyyev; Pinar Akkan
We study a source identification problem for a parabolic equation with multipoint nonlocal boundary condition. Stability estimates for the solution of abstract source identification problem are established. In application, stability estimates for the solution of the overdetermined mixed boundary value problem for multidimensional parabolic equation are obtained. The first and second order of accuracy
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Convergence Results for Optimal Control Problems Governed by Elliptic Quasivariational Inequalities Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-27 Mircea Sofonea; Domingo A. Tarzia
We consider an optimal control problem Q governed by an elliptic quasivariational inequality with unilateral constraints. We associate to Q a new optimal control problem Q˜, obtained by perturbing the state inequality (including the set of constraints and the nonlinear operator) and the cost functional, as well. Then, we provide sufficient conditions which guarantee the convergence of solutions of
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Source Conditions for Non-Quadratic Tikhonov Regularization Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-12 Markus Grasmair
Abstract In this paper, we consider convex Tikhonov regularization for the solution of linear operator equations on Hilbert spaces. We show that standard fractional source conditions can be employed in order to derive convergence rates in terms of the Bregman distance, assuming some stronger convexity properties of either the regularization term or its convex conjugate. In the special case of quadratic
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Optimal Recovery of Monotone Operators in Partially Ordered L-Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-10 Vladyslav Babenko; Vira Babenko; Oleg Kovalenko
The goal of this paper is to develop a framework that would allow one to solve the problems of optimal recovery of the monotone operators that act on a possibly most extensive class of monotone functions. The results of this work allow us to include the operators that act on the spaces of multi- and fuzzy- valued functions, as well as on the spaces of functions with values in partially ordered normed
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Operators with Property (E) as Concerns Numerical Analysis and Visualization Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-05 Gabriela Ioana Usurelu; Andreea Bejenaru; Mihai Postolache
In this paper, we study a Thakur three-step iterative process in the new context of generalized nonexpansive mappings enriched with property (E). A uniformly convex Banach space is used as underlying setting for our approach. In order to emphasize our results we offer an example of a mapping on R2 endowed with property (E) that exceeds the well known class of Suzuki mappings. By connecting the Thakur
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Analysis of Stabilized Crank-Nicolson Time-Stepping Scheme for the Evolutionary Peterlin Viscoelastic Model Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-07-08 S. S. Ravindran
The Peterlin viscoelastic model describes the motion of certain incompressible polymeric fluids. It employs a nonlinear dumbbell model with a nonlinear spring force law making it more nonlinear than other viscoelastic models. In this paper, we propose and study a fully implicit stabilized Crank-Nicolson time stepping scheme for finite element spatial discretization of the non-stationary Peterlin viscoelastic
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Proximal Point Method for Quasi-Equilibrium Problems in Banach Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-05-04 Behzad Djafari Rouhani; Vahid Mohebbi
We study the proximal point method for solving quasi-equilibrium problems in Banach spaces, which generalizes the proximal point method for equilibrium problems and quasi-variational inequalities. We propose a regularization procedure which ensures strong convergence of the generated sequence to a solution of the quasi-equilibrium problem, under standard assumptions on the problem without assuming
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Parameter Identification for a Class of Bivariate Fractal Interpolation Functions and Constrained Approximation Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-05 S. Verma; P. Viswanathan
The current article intends to study some elementary constrained approximation aspects of the bivariate fractal functions. To this end, firstly the construction of bivariate fractal interpolation functions available in the literature is revisited with a focus to obtain a parameterized family of fractal functions corresponding to a prescribed bivariate continuous function on a rectangular region in
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Optimal Recovery of Monotone Operators in Partially Ordered L-Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-10 Vladyslav Babenko; Vira Babenko; Oleg Kovalenko
The goal of this paper is to develop a framework that would allow one to solve the problems of optimal recovery of the monotone operators that act on a possibly most extensive class of monotone functions. The results of this work allow us to include the operators that act on the spaces of multi- and fuzzy- valued functions, as well as on the spaces of functions with values in partially ordered normed
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Iterated Boolean Sums of Bernstein Type Operators Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-06-10 Tuncer Acar; Ali Aral; Ioan Raşa
The approximation of functions using linear positive operators is affected by saturation. The quality of approximation offered by iterated Boolean sums increases with the regularity of the function. We present some qualitative and quantitative results concerning the approximation by such Boolean sums. The general results are illustrated by examples.
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The Exact Form of the Second Moment of Third Degree Schoenberg Spline Operators Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-05-18 Camelia Liliana Moldovan; Radu Păltănea
The article presents an explicit form for the second moment of cubic Schoenberg operators with arbitrary knots and in the particular case of equidistant knots. Applications are given for quantitative direct results in approximation and in construction of special classes of Schoenberg operators.
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Applications of Optimization Theory to Social Benefit Maximizations in Macroeconomics with Uncertainty Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-04-17 Jinlu Li; Glenn Stone
In this paper, we use the upward power preorder relation on the power sets of ordered sets to construct a mathematical social benefit maximization model in a fiscal year with respect to the initially planned fiscal budgetary policies and the practically implementation of the fiscal budgetary policies. We only consider the uncertainty case for the social benefit functions. By applying the Fan-KKM Theorem
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Sampling and Average Sampling in Quasi Shift-Invariant Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-04-06 Anuj Kumar; Sivananthan Sampath
In this paper, we study the sampling and average sampling problem in a quasi shift-invariant space VX(φ), where X is a discrete subset of R and φ is a continuously differentiable positive definite function satisfying certain decay conditions. We show that any f belonging to VX(φ) can be uniquely and stably reconstructed from its samples {f(yk):k∈Z} as well as from its average samples provided sampling
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Existence of at Least Three Distinct Weak Solutions for a Class of Nonlinear System of Fractional Differential Equations Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-03-30 Elyas Shivanian
In this article, it is concerned existence of solutions to a class of nonlinear system of fractional differential equations. It is proved the existence of at least three different weak solutions through the critical point theory and the variational method. In this way, it is applied well-known theorem proved by Bonanno and Marano on the construction of the critical set of functionals with a weak compactness
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On Ad-Nonprojection Method for Stable Approximation to Infinite-Dimensional Moore–Penrose Inverse Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-03-27 Nailin Du; Shanlin Gan
Abstract This note presents ad-nonprojection method for approximation to infinite-dimensional Moore-Penrose inverse, which includes generalized projection method as a special case. The main result (Theorem 4) gives characteristics of perfect convergence, weak perfect convergence, and uniform perfect convergence of ad-nonprojection method. This result is a generalization of several fundamental theorems
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A Data-Driven Iteratively Regularized Landweber Iteration Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-03-24 A. Aspri; S. Banert; O. Öktem; O. Scherzer
We derive and analyze a new variant of the iteratively regularized Landweber iteration, for solving linear and nonlinear ill-posed inverse problems. The method takes into account training data, which are used to estimate the interior of a black box, which is used to define the iteration process. We prove convergence and stability for the scheme in infinite dimensional Hilbert spaces. These theoretical
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Strong Convergence Theorems by Hybrid Methods for Two Noncommutative Nonlinear Mappings in Banach Spaces Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-03-20 Wataru Takahashi; Jen-Chih Yao
In this paper, using the hybrid method defined by Nakajo and Takahashi, we first obtain a strong convergence theorem for two noncommutative generic skew generalized nonspreading mappings in a Banach space. Next, using the shrinking projection method defined by Takahashi, Takeuchi and Kubota, we prove another strong convergence theorem for the mappings in a Banach space. Using these results, we get
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Further Results on the Sharp Ordering in Rings Numer. Funct. Anal. Optim. (IF 0.896) Pub Date : 2020-03-19 Xiaoji Liu; Shiqin Fu; Yaoming Yu
Abstract In this article, we will present some results relating sharp ordering (a≤♯b) and investigate the properties of one-sided cyclic ideals in rings. Necessary and sufficient conditions for the invertibility and the group invertibility of the linear combination c1a+c2b are given, where a is below b under the sharp order, a and b are elements of an algebra, and c1, c2 are elements of an arbitrary