BHASKAR-LAKSHMIKANTHAM TYPE COUPLED FIXED POINT RESULTS FOR RATIONAL CONTRACTIVE EXPRESSION USING g-MONOTONE MAPPING

Abstract

In this paper, we prove some coupled coincidence point theorems for maps satisfying contractive conditions involving a rational expression in the setting of partially ordered metric spaces using monotone property instead of the often used mixed monotone property. We also give some sufficient conditions for the existence and uniqueness of coupled coincidence points. In particular, it is shown that the results existing in the literature are extended, generalized, unified and improved by using monotone property. Also, examples are given to support these improvements. As an application, we give a result of existence and uniqueness for the solutions of a class of nonlinear integral equations.