Common fixed point theorems for nonexpansive mappings using the lower semicontinuity property
Functional Analysis
2018-11-05 v1
Abstract
Suppose that E is a Banach space, {\tau} a topology under which the norm of E becomes {\tau}-lower semicontinuous and S a commuting family of {\tau}-continuous nonexpansive mappings defined on a {\tau}-compact convex subset C of E: It is shown that the set of common fixed points of S is a nonempty nonexpansive retract of C. Along the way, a few other related fixed point theorems are derived.
Cite
@article{arxiv.1811.00792,
title = {Common fixed point theorems for nonexpansive mappings using the lower semicontinuity property},
author = {Sławomir Borzdyński},
journal= {arXiv preprint arXiv:1811.00792},
year = {2018}
}
Comments
To appear in Colloquium Mathematicum