# An Entourage Approach to the Contraction Principle in Uniform Spaces Endowed with a Graph

Source: [An Entourage Approach to the Contraction Principle in Uniform Spaces Endowed with a Graph](<https://www.sota2.com/research/paper/68fa50451e209131ce969c88>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-28T13:55:29.074Z

Authors: A. Aghanians, K. Fallahi, K. Nourouzi

Published: 2013-05-15T19:55:57.000Z

## 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.

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/1305.3600>)

[PDF](<https://arxiv.org/pdf/1305.3600.pdf>)