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 http://dx.doi.org/10.22436/jnsa.009.12.04

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2287 Downloads
• 4181 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

Keywords

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

MSC

•  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