Weak convergence of the iterations for asymptotically $G$-nonexpansive maps on Banach spaces with a graph
Functional Analysis
2022-02-28 v1 General Topology
Abstract
We have derived that on certain Banach spaces having a graph structure , the iterations for asymptotically -nonexpansive map will converge weakly towards a fixed point. This result unifies and extends several theorems on fixed points proved by various authors for class of nonexpansive and asymptotically nonexpansive maps. As an application of this result, we derive that for maps satisfying the nonexpansive condition locally on special Banach spaces, the successive approximations converge weakly towards a fixed point.
Keywords
Cite
@article{arxiv.2202.12728,
title = {Weak convergence of the iterations for asymptotically $G$-nonexpansive maps on Banach spaces with a graph},
author = {Asrifa Sultana},
journal= {arXiv preprint arXiv:2202.12728},
year = {2022}
}