COUPLED FIXED POINTS IN PARTIALLY ORDERED METRIC SPACES BY SAMET'S METHOD AND APPLICATION

Abstract

In 2006, Bhaskar and Lakshmikantham proved a fixed point theorem for a mixed monotone mapping in a metric space endowed with partial order, using a weak contractivity type of assumption. Recently Luong and Thuan proved some results of coupled fixed point that generalized main results of them. In this paper, By using the samet's method and by using different conditions we prove some coupled fixed point theorems for mapping having mixed monotone property in partially ordered metric space. Also by considering the results of Berinde and Burcut and using the main idea of Samet and Vetro extend the concept of $\alpha$-admissibility for tripled fixed point theorems in metric spaces. As an application, we discuss the existence and solution of a nonlinear integral equation.