On Quadruple Random Fixed Point Theorems in Partially Ordered Metric Spaces

Abstract

Bhaskar and Lakshmikantham in [15] introduced the concept of coupled fixed point of a mapping and investigated the existence and uniquencess of a coupled fixed point theorem in partially ordered complete metric space. Lakshmikantham and Ciric [16] defined  mixed g-monotone property and coincidence point in partially ordered metric space. V. Berinde and M. Borcut[18] introduced the concept of triple fixed point and proved some related theorems. Following this trand,  Karapinar[19] introduced the nation of quadruple fixed point. The object of this note is to prove quadruple random fixed point theorem in partially ordered metric spaces.