Related papers: The split common null point problem for generalize…

In this paper, we introduce new implicit and explicit iterative schemes which converge strongly to a unique solution of variational inequality problems for strongly accretive operators over a common fixed point set of finite family of…

We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive…

While the classic separable quotient problem remains open, we survey general results related to this problem and examine the existence of a particular infinitedimensional separable quotient in some Banach spaces of vector-valued functions,…

When optimization theorists consider optimization problems in infinite dimensional spaces, they need to deal with closed convex subsets(usually cones) which mostly have empty interior. These subsets often prevent optimization theorists from…

Let C be a nonempty, bounded, closed, and convex subset of a Banach space X and $T : C \rightarrow C$ be a monotone asymptotic nonexpansive mapping. In this paper, we investigate the existence of fixed points of T. In particular, we…

We study the problem of the existence of a common algebraic complement for a pair of closed subspaces of a Banach space. We prove the following two characterizations: (1) The pairs of subspaces of a Banach space with a common complement…

In this paper, we prove some theorems related to properties of generalized symmetric hybrid mappings in Banach spaces. Using Banach limits, we prove a fixed point theorem for symmetric generalized hybrid mappings in Banach spaces. Moreover,…

In a real Banach space, we first prove that the sum of a monotone operator of type (FPV) and maximal monotone operator Rockafellar's constraint qualification is maximal. This prove leads to the solution of most interesting long-time…

In this work we will consider integral equations defined on the whole real line and look for solutions which satisfy some certain kind of asymptotic behavior. To do that, we will define a suitable Banach space which, to the best of our…

In this paper, we introduce a novel two-point gradient method for solving the ill-posed problems in Banach spaces and study its convergence analysis. The method is based on the well known iteratively regularized Landweber iteration method…

This paper introduces a new definition of $\alpha$-monotone operators in real 2-uniformly convex and smooth Banach spaces. Based on this new definition, we establish several novel structural and analytical properties of such operators,…

In this paper we propose a resolvent splitting with minimal lifting for finding a zero of the sum of $n\ge 2$ maximally monotone operators involving the composition with a linear bounded operator. The resolvent of each monotone operator,…

In this paper, we study the existence of solutions for generalized vector quasi-equilibrium problems. Firstly, we prove that in the case of Banach spaces, the assumptions of continuity over correspondences can be weakened. The theoretical…

The split common fixed-point problem is an inverse problem that consists in finding an element in a fixed-point set such that its image under a bounded linear operator belongs to another fixed-point set. Recently Censor and Segal proposed…

The split common fixed point problems has found its applications in various branches of mathematics both pure and applied. It provides us a unified structure to study a large number of nonlinear mappings. Our interest here is to apply these…

We develop a semismooth Newton framework for the numerical solution of fixed-point equations that are posed in Banach spaces. The framework is motivated by applications in the field of obstacle-type quasi-variational inequalities and…

In this article, we propose an idea to develop some sufficient conditions for the existence and uniqueness of a positive definite common solution to a pair of non-linear matrix equations. To proceed this, we present some interesting common…

We consider the task of computing an approximate minimizer of the sum of a smooth and non-smooth convex functional, respectively, in Banach space. Motivated by the classical forward-backward splitting method for the subgradients in Hilbert…

This article investigates the convergence properties of s-numbers of certain truncations of bounded linear operators between Banach spaces. We prove a generalized version of a known convergence result for the approximation numbers of…

It is proved that the resolvent norm of an operator with a compact resolvent on a Banach space $X$ cannot be constant on an open set if the underlying space or its dual is complex strictly convex. It is also shown that this is not the case…