Coupled fixed point theorems in complete metric spaces endowed with a directed graph and application

Abstract

The purpose of this paper is to present some existence results for coupled fixed point of a (φ,ψ) —contractive condition for mixed monotone operators in metric spaces endowed with a directed graph. Our results generalize the results obtained by Jain et al. in (International Journal of Analysis, Volume 2014, Article ID 586096, 9 pages). Moreover, we have an application to some integral system to support the results.

Keywords

• coupled coincidence point
• coupled fixed point
• edge preserving
• directed graph
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