Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
5774933 | Journal of Mathematical Analysis and Applications | 2017 | 18 Pages |
Abstract
The main aim of the paper is to study some quantitative aspects of the stability of the weakâ fixed point property for nonexpansive mappings in â1 (shortly, wâ-fpp). We focus on two complementary approaches to this topic. First, given a predual X of â1 such that the Ï(â1,X)-fpp holds, we precisely establish how far, with respect to the Banach-Mazur distance, we can move from X without losing the wâ-fpp. The interesting point to note here is that our estimate depends only on the smallest radius of the ball in â1 containing all Ï(â1,X)-cluster points of the extreme points of the unit ball. Second, we pass to consider the stability of the wâ-fpp in the restricted framework of preduals of â1. Namely, we show that every predual X of â1 with a distance from c0 strictly less than 3, induces a weakâ topology on â1 such that the Ï(â1,X)-fpp holds.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Emanuele Casini, Enrico Miglierina, Åukasz Piasecki, Roxana Popescu,