Generalized compatibility in partially ordered metric spaces

Abstract

In this paper, we introduce the notion of generalized compatibility of a pair of mappings F,G:X× X→ X, where (X,d) is a partially ordered metric space. We use this concept to prove a coupled coincidence point theorem for nonlinear contractions in partially ordered metric spaces. Our work extends the paper of Choudhury and Kundu [B.S. Choudhury and A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal. 73 (2010) 2524-2531]. Some examples are also given to illustrate the new concepts and the obtained result.

Keywords

• coupled coincidence point
• generalized compatibility
• mixed monotone property
• ordered set
• complete metric space