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

Volume 9, Issue 12, pp 5950--5969
• 1706 Views

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.

Share and Cite

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

Keywords

• Coupled coincidence point
• generalized compatibility
• monotone property
• partially ordered $S$-metric space
• Geraghty-type contraction.

•  47H10
•  54H25
•  46S40

References

• [1] M. Borcut, Tripled coincidence theorems for monotone mappings in partially ordered metric spaces, Creat. Math. Inform., 21 (2012), 135--142

• [2] M. Borcut, Tripled fixed point theorems for monotone mappings in partially ordered metric spaces, Carpathian J. Math., 28 (2012), 207--214

• [3] N. V. Dung, On coupled common fixed points for mixed weakly monotone maps in partially ordered S-metric spaces, Fixed Point Theory Appl., 2013 (2013), 17 pages

• [4] T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65 (2006), 1379--1393

• [5] M. E. Gordji, E. Akbartabar, Y. J. Cho, M. Ramezani, Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory Appl., 2012 (2012), 12 pages

• [6] Z. Kadelburg, P. Kuman, S. Radenović, W. Sintunavarat, Common coupled fixed point theorems for Geraghty-type contraction mappings using monotone property, Fixed Point Theory Appl., 2015 (2015), 14 pages

• [7] Z. Kadelburg, S. Radenović, Remarks on some recent M. Borcut's results in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 6 (2015), 96--104

• [8] V. Lakshmikantham, L. Ćirić, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70 (2009), 4341--4349

• [9] S. Radenović, Bhaskar-Lakshmikantham type results for monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 96--103

• [10] S. Radenović, Coupled fixed point theorems for monotone mappings in partially ordered metric spaces, Kragujevac J. Math., 38 (2014), 249--257

• [11] S. Radenović, Some coupled coincidence points results of monotone mappings in partially ordered metric spaces, Int. J. Nonlinear Anal. Appl., 5 (2014), 174--184

• [12] S. Sedghi, N. V. Dung, Fixed point theorems on S-metric spaces, Mat. Vensnik, 66 (2014), 113--124

• [13] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in S-metric spaces, Mat. Vesnik, 64 (2012), 258--266

• [14] M. Zhou, X.-L. Liu, Coupled common fixed point theorems for Geraghty-type contraction mappings using mixed weakly monotone property in partially ordered S-metric spaces, J. Funct. Spaces, 2016 (2016), 9 pages