COUPLED AND TRIPLED FIXED POINT THEOREMS ON A METRIC SPACE ENDOWED WITH A BINARY RELATION.

The purpose of this paper is to transpose some of the results regarding the coupled fixed point theory, developed by Bhaskar and Lakshmikantham [7], using the approaches of Ben-El-Mechaiekh [2], Asgari, Mousavi [1] and Berinde [3]. The first approach replaces the partial order relation from the Ran-Reurings fixed point theorem [10] with a transitive one, the second one uses a reflexive-only relation and whereas the third one introduces the tripled fixed points. Our aim is to obtain some generalized fixed point theorems, containing a more simple symmetrical condition, also extending them for the case of tripled fixed point. [ABSTRACT FROM AUTHOR]