Abstract In this study we establish some direct connections between arbitrary positive linear operators and their corresponding nonlinear (more exactly sublinear) max-product versions, with respect to uniform and Lp convergence. There are numerous concrete examples of approximation operators, such as Bernstein-type operators, neural network operators, sampling operators and others, where the linear

Abstract In this paper, we discuss about monotone vector fields, which is a typical extension to the theory of convex functions, by exploiting the tangent space structure. This new approach to monotonicity in CAT(0) spaces stands in opposed to the monotonicity defined earlier in CAT(0) spaces by Khatibzadeh and Ranjbar [J. Aust. Math. Soc. 103(1), 70–90 (2017).] and Chaipunya and Kumam [Optimization

Abstract The main purpose of the paper is to investigate the spectra of the q−Cesàro operator Cq, where 0

Abstract We study the pointwise degree of approximation of periodic functions of bounded variation by positive linear polynomial operators. For the proof we used sub-additive majorants.

Abstract In present times, there has been a substantial endeavor to generalize the classical notion of iterated function system (IFS). We introduce a new type of non-linear contraction namely cyclic Meir-Keeler contraction, which is a generalization of the famous Banach contraction. We show the existence and uniqueness of the fixed point for the cyclic Meir-Keeler contraction. Using this result, we

Abstract In this manuscript, we consider a bivariate extension of modified ρ-Bernstein operators and obtain Voronovskaya type and Grüss Voronovskaya type theorems for these operators. Further, we determine the rate of convergence of these operators in terms of the complete and partial moduli of continuity and compute an estimate of the error in terms of the Peetre’s K-functional. Also, we define the

Abstract In the present article, we extend our study of Kantorovich type exponential sampling operators introduced in [4]. We derive the Voronovskaya type theorem and its quantitative estimates for these operators in terms of an appropriate K-functional. Further, we improve the order of approximation by using the convex type linear combinations of these operators. Finally, we provide few examples of

Abstract This article deals with almost phaseless sampling for spaces generated by B-splines with arbitrary knots. We provide a necessary and sufficient condition, which is a characterization of an almost phaseless sampling set, to admit phase recovery for almost all B-spline functions on an interval. Our results show that only N + 1 intensity measurements are sufficient to recover phase information

Abstract A large number of nonlinear and optimization problems can be reduced to altering point problems. This paper aims to introduce the parallel normal S-iteration technique and study its convergence rates for solving such problems in infinite-dimensional Hilbert spaces under practical assumptions. We place particular emphasis on the parallel splitting method for the sum of two maximal monotone

Abstract The aim of the present paper is to study the existence and asymptotic behavior of the solutions of some functional integral equations which contain a number of classical nonlinear integral equations as special cases. The main tools used in our considerations are the concept of a measure of noncompactness and the classical Schauder fixed point principle. The investigations of the paper are

Abstract Critical point results for a 2nth-order differential equation with Sturm-liouville operator is exploited in order to prove that a suitable class possesses at least one solution under an asymptotical behavior of the potential of the nonlinear term at zero, and also possesses infinitely many solutions under some hypotheses on the behavior of the potential of the nonlinear term at infinity. Some

Abstract In this paper, we recall the main results of the Fourier transform on the quaternionic Heisenberg group, then we introduce the notion of the Gabor transform on this group and study some of its properties. Finally, we prove some uncertainty principles associated with this transform.

Abstract Using the technique associated with the classical Schauder fixed point theorem we demonstrate the existence of solutions of a class of quadratic integral equation of Fredholm type in Hölder spaces. Moreover, one useful example is discussed to justify our theoretical results.

Abstract In this paper, we consider a penalty method for a class of differential hemivariational inequalities in reflexive Banach spaces, governed by a set of constraints. First, we recall the existence and uniqueness result of the differential hemivariational inequality. Further, we introduce a penalized problem without constraints and we prove that, as a penalty parameter tends to zero, the solution

Abstract The real Ginzburg–Landau equation is studied in this article. We proceed and use the Galerkin method in combination with the compactness theorem to show that the solution of this problem exists and is unique in appropriate Sobolev spaces. This is proceeded by the designing of a reliable nonlinear numerical scheme from the afore mentioned problem and further show that this scheme is stable

Abstract The purpose of this article is to study convergence analysis of quasi-variational inequalities using a projection-type method coupled with inertial extrapolation step. First, we give strong convergence analysis of the sequence of iterates generated by our proposed method to the unique solution of quasi-variational inequality under some mild assumptions. Later, we show that the sequence converges

Abstract Let L(X,Y) be the space of bounded linear operators between real Banach spaces X, Y. For a closed subspace Z⊂Y, we partially solve the operator version of Birkhoff–James orthogonality problem, if T∈L(X,Y) is orthogonal to L(X,Z), when does there exist a unit vector x0 such that ||T(x0)||=||T|| and T(x0) is orthogonal to Z? In order to achieve this we first develop a compact optimization for

Abstract In this paper, a new system of variational inclusions involving set-valued quasi-contractive, lower semi-continuous mappings with nonempty closed and convex values is introduced and studied in real Banach spaces. First, both the existence of fixed points of the set-valued quasi-contractive mappings and the solution of the system of variational inclusions are proved. Then, using the existence

Abstract In this paper, hybrid best proximity points for a class of proximally mixed monotone set-valued mappings are discussed. In order to get rid of the fetter of continuity, we introduce the proximally ordered contraction instead of various proximal distance contractions widely applied in recent literatures and present some new existence and iterative approximation theorems of best proximity points

Abstract Recently, Moudafi introduced the split equality problem (SEP): find x∈C,y∈Q such that Ax = By. In this paper, we show that finding a solution of the SEP is equivalent to finding a solution of a coupled fixed-point equation which is an extension of the coupled equation proposed by Yu and Wang. Based on this coupled fixed-point equation, we propose two new relaxed alternating algorithms for

Abstract We prove several important results concerning existence and uniqueness of pseudo almost automorphic (paa) solutions with measure for integro-differential equations with reflection. We use the properties of almost automorphic functions with measure and the Banach fixed point theorem, and we discuss two linear and nonlinear cases. We conclude with an example and some observations.

Abstract In this paper, we present two main results about best proximity points for multivalued mappings. First, taking into account Klim and Wardowski’s approach in fixed-point theory, we obtain a new result for multivalued mappings which includes the main theorem of Kamran [Kamranm, T. (2009). Mizoguchi–Takahashi’s type fixed point theorem. Comput. Math. Appl. 57(3):507–511]. Second, combining this

Abstract In this paper, we introduce a new system of variational inclusion problems called system of generalized set-valued variational inclusion problems involving αβ-H((.,.),(.,.))-mixed accretive mapping in q-uniformly smooth Banach spaces. By means of proximal-point mapping method, we prove the existence of solution of this system of variational inclusions. Further, we propose an iterative algorithm

Abstract We study the split common fixed point problem with multiple output sets in Hilbert spaces. In order to solve this problem, we propose two new algorithms and establish two strong convergence theorems for both of them. Moreover, using these methods, we also remove the assumptions imposed on the norm of the transfer operators.

Abstract In this article, efficient methods are derived for seeking numerical solution to the time fractional convection-diffusion-reaction equation whose solution very likely exhibits a weak regularity at the starting time. Here, the time fractional derivative in the Caputo sense with order in (0, 1) is discretized by the finite difference methods with uniform and non-uniform meshes and the spatial

Abstract The aim of this article is to introduce new iterative algorithms for finding a common solution from the set of equilibrium points of an equilibrium problem and of singularities of an inclusion problem on Hadamard manifolds. We discuss some particular cases of the problem with the proposed algorithms. The convergence results of a sequence generated by the proposed algorithms are proved under

Abstract In this paper, an adaptive grid method for singularly perturbed Volterra integro-differential equations exhibiting a boundary layer is studied. At first, based on an arbitrary nonuniform mesh, we use the classical backward Euler formula to discrete the first-order derivative part and the left rectangle formula to approximate the integral part, respectively. Meanwhile, it is shown from the

Abstract In this paper, we introduce a novel dual variable algorithm accelerated via inertial extrapolation for solving the generalized split inverse problem given as a task of finding the common null point equality of finite family of inverse-strongly monotone mappings in Hilbert spaces. The proposed method uses the dual variable and self-adaptive technique, along with an inertial strategy which aims

Abstract This paper discusses differential stability of convex discrete optimal control problems with mixed constraints. Among the obtained results, we give formulas for exact computing the subdifferential and the singular subdifferential of the optimal value function via suitable multiplier sets.

Abstract Using the monotonicity methods, we obtain conditions for the existence of the unique weak solution of Dirichlet problem {Δu(x)+a(x)u(x)=f(x,u(x))x∈V\V0u|V0=0, considered on the Sierpiński gasket. We argue for the optimality of some assumptions. Some Lyapunov-type inequalities are also given. We also consider a problem with parameters and we prove the theorem about continuous dependence on

Abstract In this paper. we consider fuzzy Volterra integral equation of the second kind with weakly singular kernel. We prove existence and uniqueness of the solution. When analyzing the convergence of a numerical method for a given integral equation one needs information about the smoothness of the exact solution. We describe the smoothness of the solution, assuming that the sign of the kernel can

Abstract We have modified our previously developed fourth order method to approximate solution of systems of equations including non-differentiable ones. The most recent article by Kumar et al. (Numer. Algor. 86:1051–1070, 2021) compared fourth order and seventh order methods to show the efficiency of their fourth order. We have shown that our method compares favorably with methods in the literature

Abstract The essential importance of the best proximity point theory is that “best proximity point theory” appears in the coincidence of “metric fixed point theory” and “optimization theory.” So finding best proximity points of mappings satisfying different type of contractive conditions in different structures is one of the fascinating research topics. For this, in this article, we first introduce

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 work, we study an inverse nodal problem for a differential pencil with boundary condition depends on eigenparameter. We show that there exists a solution of the problem that satisfied the conditions. Also, we give eigenvalues, nodal points and some formulas for qn(x). Although there were given some results for this type problem, we think that inverse nodal problems have not solved

Abstract In this paper, we fully characterize the duality mapping over the space of matrices that are equipped with Schatten norms. Our approach is based on the analysis of the saturation of the Hölder inequality for Schatten norms. We prove in our main result that, for p∈(1,∞), the duality mapping over the space of real-valued matrices with Schatten-p norm is a continuous and single-valued function

Abstract Kohlenbach and Leuştean have shown in 2010 that any asymptotically nonexpansive self-mapping of a bounded nonempty UCW-hyperbolic space has a fixed point. In this paper, we adapt a construction due to Moloney in order to provide a sequence that converges strongly to such a fixed point.

Abstract In the present paper, we have proved a basic theorem on the absolute Riesz summability factors of infinite series by using a wider class of power increasing sequences and then we applied this new result to the trigonometric Fourier series. Some new results are also obtained concerning the factored infinite series and trigonometric Fourier series.

Abstract This work studies the approximate controllability of a class of first-order retarded semilinear differential equations with delays in control and nonlocal conditions. First we deduce the existence of mild solutions using fixed point approach. For this, the nonlinear function is supposed to be locally Lipschitz, which is a weaker condition than Lipschitz continuity. Controllability results

Abstract In this paper, we propose an iterative method for solving split equality problems in the nonconvex setting. Relying on the associated penalized optimization formulation, we study a relevant iterative algorithm, which is nothing else than a generalized CQ-algorithm, and prove that its global convergence is guaranteed in the nonconvex setting under mild conditions on the problems data. Then

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 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 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 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, 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 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 ∑anλn 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 FG-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