Abstract
In this paper, we introduce a new contractive condition for a pair of commuting mappings in partially ordered G-metric spaces. Some new coupled coincidence point and coupled common fixed point theorems are obtained. An example is given to support the usability of our results. The results presented in this paper generalize and improve the corresponding results of Nashine and Shatanawi from partially ordered metric spaces to partially ordered G-metric spaces. MSC:47H10, 54H25, 54E50.
Highlights
1 Introduction and preliminaries In, Ran and Reurings [ ] showed the existence of fixed points of nonlinear contraction mappings in metric spaces endowed with a partial ordering and presented applications of their results to matrix equations
It is well known that fixed point theory in partially ordered metric spaces as one of the most important tools of nonlinear analysis has been widely applied to matrix equations, ordinary differential equations, fuzzy differential equations, integral equations and intermediate value theorems
Based on the concept of a G-metric space, many authors obtained many fixed point and common fixed point theorems for the mappings satisfying different contractive conditions; see [ – ] for more details
Summary
Introduction and preliminariesIn , Ran and Reurings [ ] showed the existence of fixed points of nonlinear contraction mappings in metric spaces endowed with a partial ordering and presented applications of their results to matrix equations. Many authors obtained many coupled coincidence and coupled fixed point theorems in ordered metric spaces; see [ – ] and the references therein.
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