In this paper, we present a new iterative scheme for finding a common element of the solution set F of the split feasibility problem and the fixed point set F(T) of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate condition...

• Positivity: N(v) ≥ 0 with equality if and only if v = 0. • Positive Homogeneity: N(αv) = |α|N(v). • Triangle Inequality: N(x1 + x2) ≤ N(x1) +N(x2). If N is a norm for V then we call ρ N (x1, x2) := N(x1−x2) the associated distance function (or metric) for V . A vector space V together with some a choice of norm is called a normed space, and the norm is usually denoted by ‖ ‖. If V is complete...

We prove that if C ⊂ R is of class C and uniformly convex, then the Cheeger set of C is unique. The Cheeger set of C is the set which minimizes, inside C, the ratio perimeter over volume.

Recently, Chang, et al introduce the concept of total asymptotically nonexpansive mapping which contain the asymptotically nonexpansive mapping. The purpose of the paper is to analyze a three-step iterative scheme for total asymptotically nonexpansive mapping in uniformly convex hyperbolic spaces. Meanwhile, we obtain a ∆-convergence theorem of the three-step iterative scheme for total asymptot...

We give a general result on the behavior of spreading models in Banach spaces which coarse Lipschitz-embed into asymptotically uniformly convex spaces. We use this result to study the uniqueness of the uniform structure in p-sums of finite-dimensional spaces for 1 < p < ∞; in particular we give some new examples of spaces with unique uniform structure.

We prove that if a metric probability space with a usual concentration property embeds into a Banach space X, then X has a proportional Euclidean subspace. In particular, this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings spaces with concentration properties (i.e. uniformly convex spaces) into l ∞, thus providing an ”isomorphic” extension to ...

Recently, in [4] the author has proved that if B is an open unit ball in a Cartesian product l2× l2 furnished with the lp-norm ‖ · ‖ and kB is the Kobayashi distance on B, then the metric space (B,kB) is locally uniformly linearly convex. In this paper, we introduce this kind of local uniform convexity in bounded convex domains in complex reflexive Banach spaces and we apply this notion in the ...

An existence theorem for a fixed point of an α-nonexpansive mapping of a nonempty bounded, closed and convex subset of a uniformly convex Banach space is recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishihawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also exten...

A classical problem in functional analysis has been to give a geometric characterization of reflexivity for a Banach space. The first result of this type was D.P. Milman’s [Mil] and B.J. Pettis’ [P] theorem that a uniformly convex space is reflexive. While perhaps considered elementary today it illustrated how a geometric property can be responsible for a topological property. Of course a Banac...

Let C be a bounded, closed, convex subset of a uniformly convex Banach space X. We investigate the convergence of the generalized Krasnosel’skiiMann and Ishikawa iteration processes to common fixed points of pointwise Lipschitzian semigroups of nonlinear mappings Tt : C → C. Each of Tt is assumed to be pointwise Lipschitzian, that is, there exists a family of functions αt : C → [0,∞) such that ...