Coupled coincidence point results for Geraghtytype 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. Radenović, 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.