Geodesic
Coupled coincidence point results for Geraghty-type contraction by using monotone property in partially ordered $S$-metric spaces
Zhou, Mi1 ; Liu, Xiao-lan2 ; Dolićanin-Dekić, Diana3 ; Damjanović, Boško4
1 School of Science and Technology, Sanya College, 572022, Sanya, Hainan, China
2 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
3 Faculty of Technical Science, University of Pristina-Kosovska Mitrovica, Pristina, Serbia
4 Faculty of Agriculture, University of Belgrade, Belgrade, Serbia
Journal of nonlinear sciences and its applications, Tome 9 (2016) no. 12, p. 5950-5969.

Voir la notice de l'article provenant de la source International Scientific Research Publications

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.
DOI : 10.22436/jnsa.009.12.04
Classification : 47H10, 54H25, 46S40
Keywords: Coupled coincidence point, generalized compatibility, monotone property, partially ordered \(S\)-metric space, Geraghty-type contraction.

Zhou, Mi 1 ; Liu, Xiao-lan 2 ; Dolićanin-Dekić, Diana 3 ; Damjanović, Boško 4

1 School of Science and Technology, Sanya College, 572022, Sanya, Hainan, China
2 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
3 Faculty of Technical Science, University of Pristina-Kosovska Mitrovica, Pristina, Serbia
4 Faculty of Agriculture, University of Belgrade, Belgrade, Serbia 
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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 its applications, Tome 9 (2016) no. 12, p. 5950-5969. doi : 10.22436/jnsa.009.12.04. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.009.12.04/

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