Abstract In order to calculate the Wiener integrals for functionals on Wiener space, one can usually apply the change of variable theorem. But, there are many functionals that are difficult or impossible to calculate even when using the change of variable formula. In order to solve this problem, we establish an evaluation formula via the Fourier-type functionals on Wiener space. We then present various

Abstract For the extended linear complementarity problem (ELCP), we establish a global error bound estimation for ELCP under milder condition. Based on this, we propose a smoothing algorithm for solving the problem. The algorithm is shown to be globally convergent and quadratically convergent rate without nondegenerate assumption. The result obtained in this paper extend the existing ones for the ELCP

Abstract In this paper, we are concerned with a nonsmooth semivectorial bilevel optimization problem (P). Using a scalarization technique, we transform the lower-level problem into several scalar optimization problems (Pzxs). We give necessary optimality condition in terms of the limiting subdifferentials and the limiting normal cones. Completely detailed first-order necessary optimality conditions

Abstract Using proof-theoretical techniques, we analyze a proof by Hong-Kun Xu regarding a result of strong convergence for the Halpern type proximal point algorithm. We obtain a rate of metastability (in the sense of Terence Tao) and also a rate of asymptotic regularity for the iteration. Furthermore, our final quantitative result bypasses the sequential weak compactness argument present in the original

Abstract In this article, we establish theory of Parseval framelets associated to generalized multiresolution analysis (GMRA) in the setting of reducing subspace for the local field of positive characteristics (LFPC). We develop the unitary extension principle for Parseval framelets associated to GMRA on LFPC. The procedure for the construction of Parseval framelets is also established. An example

Abstract Sweldens and Piessens [23 Sweldens, W., Piessens, R. (1992). Calculation of the wavelet decomposition using quadrature formulae. CWI Quarterly. 5(1):33–52. [Google Scholar]] gave the crucial relationship between the first and the second scaling moment in order to derive an effective one-point quadrature formula to reproduce polynomials up to degree 2. Finěk [6 Finěk, V. (2005). Quadrature

Abstract In this paper, by using regular summability methods we modify the Bernstein–Chlodovsky operators in order get more general and powerful results than the classical aspects. We study Korovkin-type approximation theory on weighted spaces. As a special case, it is possible to Cesàro approximate (arithmetic mean convergence) to the test function e2(x)=x2 although it fails for the classical Bernstein–Chlodovsky

Abstract We propose definitions of well-posedness under perturbation in terms of suitable asymptotically solving sequences, not embedding a given problem into a parameterized family. When considering in detail quasi-equilibrium and quasi-optimization problems as well as optimization problems with equilibrium constraints, we establish sufficient conditions for both well-posedness and unique well-posedness

Abstract In this paper, we consider the well-posedness and approximation for nonhomogeneous fractional differential equations in Banach spaces E. Firstly, we get the necessary and sufficient condition for the well-posedness of nonhomogeneous fractional Cauchy problems in the spaces C0β([0,T];E). Secondly, by using implicit difference scheme and explicit difference scheme, we deal with the full discretization

Abstract The aim of this study is to give some new bilinear Hardy–Steklov type integral inequalities with functions of two variables by using the operator STdefined by (1.4).

Abstract The purpose of this paper is to introduce a new splitting iterative algorithm for finding a common solution of a system of quasi-variational inclusion problems, equilibrium problems and fixed point for quasi-nonexpansive mappings in Hadamard manifolds. It is shown that under mild conditions, the iterative sequence generated by the proposed algorithm converges to a common solution. As applications

Abstract In the present paper we establish a link between the Jain-Pethe operators and its Kantorovich type integral modification, by applying the methods of finite differences. We also consider a modification of the Kantorovich variant, preserving affine functions and establish some direct results in weighted spaces.

Abstract Let Δ−n be the backward difference operator of order −n. In this paper, we study some properties of the matrix domain associated with this operator and after computing α-, β-, γ-duals, we characterize some matrix classes on this space. Moreover, we investigate the problem of finding the norm of well-known operators such as Cesàro and Hilbert from ℓp(Δ−n) into ℓp.

Abstract In this paper, we introduce a novel extension of the Bernstein-Kantorovich-Stancu type operator of degree n with the help of multiple shape parameters. Voronovskaja and Grüss-Voronovskaja type approximation theorems are examined via Ditzian-Totik moduli of smoothness. We investigate basic statistical convergence properties with respect to a non-negative regular summability matrix. Moreover

Abstract In this article, our aim is to obtain weak solutions for a class of Kirchhoff-type problems −M(∫ΩA(x,∇u)dx)div a(x,∇u)=f(x,u) inΩ, by using the theory of Young measures.

Abstract This paper presents a general theorem dealing with absolute Cesàro summability of the series ∑ a n λ n under weaker conditions.

Abstract In this paper, the concept of p-convex function based on the definition of p-convex sets is given. Then fundamental characterizations and some operational properties of p-convex functions are presented. Furthermore, the relations between p-convex functions for different p values are obtained.

Abstract We investigate the relation between the convergence of the localized Baskakov operators and the number of their terms N + 1. We obtain the limit functions and the approximation orders by the localized Baskakov operators under some conditions for N. A new estimate about the kernel of the Baskakov operators is achieved by using one of the central limit theorems in probability theory as well

Abstract In this paper, we provide an alternative approach to establish the solution existence and uniqueness for elliptic variational-hemivariational inequalities. The new approach is based on elementary results from functional analysis, and thus removes the need of the notion of pseudomonotonicity and the dependence on surjectivity results for pseudomonotone operators. This makes the theory of elliptic

Abstract In this article, we first provide some sufficient conditions, and necessary and sufficient conditions for K-woven frames to be preserved under a bounded linear operator and particularly, we report that applying two different operators to K-woven frames can leave them K-woven. Several new methods on the construction of K-woven frames are also presented. Finally we show that the perturbation

Abstract Best proximity results for cyclic and noncyclic F G -contractive operators in (strictly convex) Banach spaces are obtained via the measure of noncompactness. The work extends some of recent investigations in this direction. The obtained results are applied to investigation of optimum solutions for a system of second order differential equations with two initial conditions followed by an example

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.

Abstract In this article, we establish theory of Parseval framelets associated to generalized multiresolution analysis (GMRA) in the setting of reducing subspace for the local field of positive characteristics (LFPC). We develop the unitary extension principle for Parseval framelets associated to GMRA on LFPC. The procedure for the construction of Parseval framelets is also established. An example

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

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.

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.

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

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

(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.

(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.

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.

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

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

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

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

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

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

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

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

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.

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.

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

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

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

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

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.

(2020). Special Issue Research on Generalized Inverses in China. Numerical Functional Analysis and Optimization. Ahead of Print.

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

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

Abstract 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

Abstract 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

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

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.

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

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.

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

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

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

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

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.