Related papers: On proximal uniform normal structure and relativel…

The purpose of this article is to study the existence of a coincidence point for two mappings defined on a nonempty set and taking values on a Banach space using the fixed point theory for nonexpansive mappings. Moreover, this type of…

We study geometric properties of the Banach space $\mathcal{R}$ constructed recently by C.~Read (arXiv 1307.7958) which does not contain proximinal subspaces of finite codimension greater than or equal to two. Concretely, we show that the…

Very recently, Berinde and P\u{a}curar obtained in [V. Berinde and M. P\u{a}curar, Approximating fixed points of enriched contractions in Banach spaces. Journal of Fixed Point Theory and Applications. \textbf{22}(2) (2020), 1--10.] an…

Let \Sigma be a compact Riemann surface with n distinguished points p_1,...,p_n. We prove that the set of n-tuples (\phi_1,...,\phi_n) of univalent mappings \phi_i from the open unit disc into \Sigma mapping 0 to p_i, with non-overlapping…

We investigate necessary and sufficient conditions for a nonexpansive map $f$ on a Banach space $X$ to have surjective displacement, that is, for $f - \mathrm{id}$ to map onto $X$. In particular, we give a computable necessary and…

We study the extremality of nonexpansive mappings on a nonempty bounded closed and convex subset of a normed space (therein specific Banach spaces). We show that surjective isometries are extremal in this sense for many Banach spaces,…

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…

Let $C$ be a nonempty closed and convex subset of a uniformly smooth and uniformly convex real Banach space $E$ with dual space $E^*$. We present a novel hybrid method for finding a common solution of a family of equilibrium problems, a…

This paper is devoted to the study of strongly quasinonexpansive mappings in an abstract space and a Banach space.

This paper deals with the solution of large classes of systems of nonlinear partial differential equations (PDEs) in spaces of generalized functions that are constructed as the completion of uniform convergence spaces. The existence result…

We study the structure of the space of coarse Lipschitz maps between Banach spaces. In particular we introduce the notion of norm attaining coarse Lipschitz maps. We extend to the case of norm attaining coarse Lipschitz equivalences, a…

The aim of this paper is to present two tools, Theorems 4 and 7, that make the task of finding equivalent polyhedral norms on certain Banach spaces easier and more transparent. The hypotheses of both tools are based on countable…

Some known fixed point theorems for nonexpansive mappings in metric spaces are extended here to the case of primitive uniform spaces. The reasoning presented in the proofs seems to be a natural way to obtain other general results.

In this paper the theory of uniformly convex metric spaces is developed. These spaces exhibit a generalized convexity of the metric from a fixed point. Using a (nearly) uniform convexity property a simple proof of reflexivity is presented…

We introduce and investigate an iterative scheme for approximating common fixed point of a family of Bregman relatively-nonexpansive mappings in real reflexive Banach spaces. We prove strong convergence theorem of the sequence generated by…

Definition. A symmetric with respect to 0 bounded closed convex set A in a finite dimensional normed space X is called a sufficient enlargement for X (or of B(X)) if for arbitrary isometric embedding of X into a Banach space Y there exists…

In the setting of CAT(k) spaces, common fixed point iterations built from prox mappings (e.g. prox-prox, Krasnoselsky-Mann relaxations, nonlinear projected-gradients) converge locally linearly under the assumption of linear metric…

In this paper, we investigate the existence of fixed points for asymptotically nonexpansive mappings with center 0 defined on closed convex subsets of various Banach spaces. Three applications are given. Firstly, we prove that our results…

This paper provides a fixed point theorem and iterative construction of a common fixed point for a general class of nonlinear mappings in the setup of uniformly convex hyperbolic spaces. We translate a multi-step iteration, essentially due…

In the first part of the paper we study the structure of Banach spaces with a conditional spreading basis. The geometry of such spaces exhibit a striking resemblance to the geometry of James' space. Further, we show that the averaging…