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


Authors

Mi Zhou - School of Science and Technology, Sanya College, 572022, Sanya, Hainan, China. Xiao-lan Liu - College of Science, Sichuan University of Science and Engineering, 643000, Zigong, Sichuan, China. - Sichuan Province University Key Laboratory of Bridge Non-destruction Detecting and Engineering Computing, Zigong, Sichuan 643000, China. Diana Dolićanin-Dekić - Faculty of Technical Science, University of Pristina-Kosovska Mitrovica, Pristina, Serbia. Boško Damjanović - Faculty of Agriculture, University of Belgrade, Belgrade, Serbia.


Abstract

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.


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ISRP Style

Mi Zhou, Xiao-lan Liu, Diana Dolićanin-Dekić, Boško Damjanović, Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered \(S\)-metric spaces, Journal of Nonlinear Sciences and Applications, 9 (2016), no. 12, 5950--5969

AMA Style

Zhou Mi, Liu Xiao-lan, Dolićanin-Dekić Diana, Damjanović Boško, Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered \(S\)-metric spaces. J. Nonlinear Sci. Appl. (2016); 9(12):5950--5969

Chicago/Turabian Style

Zhou, Mi, Liu, Xiao-lan, Dolićanin-Dekić, Diana, Damjanović, Boško. "Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered \(S\)-metric spaces." Journal of Nonlinear Sciences and Applications, 9, no. 12 (2016): 5950--5969


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