Fixed point theorems and convergence theorems for a generalized nonexpansive mapping in uniformly convex Banach spaces
Functional Analysis
2020-07-07 v1 Analysis of PDEs
Abstract
In this paper, we prove the existence of fixed points of mappings satisfying the condition (Da), a kind of generalized nonexpansive mappings, on a weakly compact convex subset in a Banach space satisfying Opial's condition. And we use Sahu([6]) and Thakur([10])'s iterative scheme to establish several convergence theorems in uniformly convex Banach spaces and give an example to show that this scheme converges faster than the scheme in [1]
Cite
@article{arxiv.2007.02001,
title = {Fixed point theorems and convergence theorems for a generalized nonexpansive mapping in uniformly convex Banach spaces},
author = {Chang Il Rim and Jong Gyong Kim},
journal= {arXiv preprint arXiv:2007.02001},
year = {2020}
}
Comments
10 pages, 1 figure, 1 table