2 research outputs found
An Entourage Approach to the Contraction Principle in Uniform Spaces Endowed with a Graph
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.Comment: 20 page