Coupled coincidence and coupled common fixed point theorems on a metric space with a graph

Fixexd point theory and applications

Pradip Debnath¹  Pramod K Das¹  Dakjum Eshi¹ 

[1] Department of Mathematics, North Eastern Regional Institute of Science and Technology, Nirjuli, India

关键词: coupled fixed point;    coupled coincidence point;    coupled common fixed point;    metric space with a graph;    55M20;    54H25;    47H09;   

DOI  :  10.1186/s13663-016-0530-7

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, our aim is to introduce the concept of G-g-contraction mapping and prove some coupled coincidence and coupled common fixed point theorems for nonlinear contraction mappings in the new set up of partially ordered complete metric spaces endowed with a directed graph. As an application, we apply our results to present an existence theorem for solution of some particular integral equations. Our paper is inspired by the work of Chifu and Petrusel (Fixed Point Theory Appl. 2014:151, 2014); the authors introduced the concept of a coupled fixed point. In the current paper, however, we have established the results by introducing the new notion of a coupled coincidence fixed point instead of the coupled fixed point in the setting of a partially ordered complete metric space with graph.

【 授权许可】

CC BY