Surveys in Mathematics and its Applications

ISSN1842-6298 (electronic), 1843-7265 (print)

Volume 11 (2016), 77 -- 92

This work is licensed under a Creative Commons Attribution 4.0 International License.## GENERALIZED COMPATIBILITY IN PARTIALLY ORDERED METRIC SPACES

## Hassen Aydi and Manel Jellali

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.2010 Mathematics Subject Classification:54H25; 47H10

Keywords:Coupled coincidence point; generalized compatibility; mixed monotone property; ordered set; complete metric space

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University of Dammam, Department of Mathematics.

College of Education of Jubail, P.O: 12020, Industrial Jubail 31961, Saudi Arabia.

e-mail: hmaydi@uod.edu.sa

Manel Jellali

University of Dammam, Department of Mathematics.

College of Education of Jubail, P.O: 12020, Industrial Jubail 31961, Saudi Arabia.

e-mail: majellali@uod.edu.sa