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

Abstract

Abstract:The purpose of this paper is to present some existence results for coupled fixed point of a .'; / 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.

Some Results on N-Tupled Coincidence and Fixed Points of Graphs on Metric Spaces and an Application to Integral Equations

“…In this paper, we will obtain more general results of Kir et al [13], which are common N-tupled coincidence points and common N-tupled fixed points of operators satisfying ( , )−contractive condition in metric spaces endowed with a digraph.…”

“…In fact, this result is true for only even n but not for odd ones. Recently, Kir et al [13] considered the existence of a coupled fixed point of ( , )−contractive mappings endowed with a digraph and applied the obtained results to the system of two integral equations. There already exists an extensive literature on this topic.…”

Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

“…ere are many interesting coupled fixed-point theorems concerning some other type of contraction mappings, see [5][6][7][8][9][10].…”

Existence Fixed Point Solutions for C-Class Functions in Bipolar Metric Spaces With Applications

“…Bhaskar and Lakshmikantham [2] developed a novel fixed point theorem for mixed monotone mapping in a metric space with partial ordering after using a weak contractivity condition. For further information on coupled fixed point outcomes, see the study results ( [3], [4], [5], [6], [7], [8], [9]) and relevant references.…”