Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered S-metric spaces

In this paper, we introduce a new concept of generalized compatibility for a pair of mappings defined on a product S-metric and prove certain coupled coincidence point results for mappings satisfying Geraghty type contraction by using g-monotone instead of the usually mixed monotone property. We also give some sufficient conditions for the uniqueness of a coupled coincidence point. Our results generalize the corresponding results of Zhou and Liu [M. Zhou, X.-L. Liu, J. Funct. Spaces, 2016 (2016), 9 pages], without mixed weakly monotone property and Kadelburg et al. [Z. Kadelburg, P. Kuman, S. Radenovic, W. Sintunavarat, Fixed Point Theory Appl., 2015 (2015), 14 pages] from usually metric to S-metric. An illustrative example is presented to support our results. (C) 2016 All rights reserved.