An Entourage Approach to the Contraction Principle in Uniform Spaces Endowed with a Graph
General Topology
2013-05-16 v1
Abstract
In this paper, we study Banach contractions in uniform spaces endowed with a graph and give some sufficient conditions for a mapping to be a Picard operator. Our main results generalize some results of [J. Jachymski, "The contraction principle for mappings on a metric space with a graph", Proc. Amer. Math. Soc. 136 (2008) 1359-1373] employing the basic entourages of the uniform space.
Keywords
Cite
@article{arxiv.1305.3600,
title = {An Entourage Approach to the Contraction Principle in Uniform Spaces Endowed with a Graph},
author = {A. Aghanians and K. Fallahi and K. Nourouzi},
journal= {arXiv preprint arXiv:1305.3600},
year = {2013}
}
Comments
20 pages