New coupled and common coupled fixed point results with generalized \({c}\)-distance on cone \({b}\)-metric spaces

Volume 25, Issue 3, pp 209--218 http://dx.doi.org/10.22436/jmcs.025.03.01

Publication Date: June 16, 2021 Submission Date: January 21, 2021 Revision Date: April 11, 2021 Accteptance Date: May 06, 2021

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)

• 936 Downloads
• 2187 Views

Authors

Sahar M. Abusalim - Department of Mathematics, College of Sciences and Arts, Jouf University, Al-qurayyat, KSA. Zaid M. Fadail - Department of Mathematics, Faculty of Education, Thamar University, 87246, Thamar, Republic of Yemen.

Abstract

In this paper, we prove the existence and uniqueness of common coupled fixed point and coupled fixed point in cone \({b}\)-metric spaces with generalized \({c}\)-distance. Our results extend and generalize several well-known comparable results in literature. We provide one example to support our obtained results.

Share and Cite

Keywords

• Cone \({b}\)-metric spaces
• coupled fixed points
• coupled coincidence points
• common coupled fixed points
• generalized \({c}\)-distance

MSC

•  47H10
•  54H25

References

• [1] M. Abbas, M. A. Khan, S. Radenovic, Common coupled fixed point theorems in cone metric spaces for w-compatible mappings, Appl. Math. Comput., 217 (2010), 195--202
  • View Article
  • MathSciNet


• [2] A. G. B. Ahmad, Z. M. Fadail, M. Abbas, Z. Kadelburg, S. Radenovic, Some fixed and periodic points in abstract metric spaces, Abstr. Appl. Anal., 2012 (2012), 15 pages
  • View Article
  • MathSciNet


• [3] I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Ul’yanovsk. Gos. Ped. Inst., Ul’yanovsk, 30 (1989), 26--37
  • MathSciNet
  • Google Scholar


• [4] B. Baoa, S. Xu, L. Shi, V. C. Rajic, Fixed point theorems on generalized c-distance in ordered cone b-metric spaces, Int. J. Nonlinear Anal. Appl., 6 (2015), 9--22
  • View Article
  • Google Scholar


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


• [6] Y. J. Cho, R. Saadati, S. Wang, Common fixed point theorems on generalized distance in ordered cone metric spaces, Comput. Math. Appl., 61 (2011), 1254--1260
  • View Article
  • MathSciNet


• [7] A. S. Cvetkovic, M. P. Stanic, S. Dimitrijevic, S. Simic, Common fixed point theorems for four mappings on cone metric type space, Fixed Point Theory Appl., 2011 (2011), 15 pages
  • View Article
  • MathSciNet


• [8] M. Đorđević, D. Đorić, Z. Kadelburg, S. Radenović, D. Spasić, Fixed point results under c-distance in tvs-cone metric spaces, Fixed Point Theory Appl., 2011 (2011), 9 pages
  • View Article
  • MathSciNet
  • Google Scholar


• [9] Z. M. Fadail, S. M. Abusalim, T-Reich Contraction and Fixed Point Results in Cone Metric Spaces with c-Distance, Int. J. Math. Anal., 11 (2017), 397--405
  • View Article
  • Google Scholar


• [10] Z. M. Fadail, A. G. B. Ahmad, Coupled fixed point theorems of single-valued mapping for c-distance in cone metric spaces, J. Appl. Math., 2012 (2012), 20 pages
  • View Article
  • MathSciNet


• [11] Z. M. Fadail, A. G. B. Ahmad, Common coupled fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstr. Appl. Anal., 2012 (2012), 24 pages
  • View Article
  • MathSciNet


• [12] Z. M. Fadail, A. G. B. Ahmad, Fixed point theorems of T-contraction mappings under c-distance in cone metric spaces, AIP Conf. Proc., 1571 (2013), 1030--1034
  • View Article
  • Google Scholar


• [13] Z. M. Fadail, A. G. B. Ahmad, Coupled coincidence point and common coupled fixed point results in cone b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 14 pages
  • View Article
  • MathSciNet


• [14] Z. M. Fadail, A. G. B. Ahmad, New Coupled Coincidence Point and Common Coupled Fixed Point Results in Cone Metric Spaces with c-Distance, Far East J. Math. Sci., 77 (2013), 65--84
  • View Article


• [15] Z. M. Fadail, A. G. B. Ahmad, Fixed Point Results of T-Kannan Contraction On Generalized Distance in Cone Metric Spaces, Proceedings of the 3rd International Conference on Mathematical Sciences, AIP Conf. Proc., 1602 (2014), 680--683
  • View Article
  • Google Scholar


• [16] Z. M. Fadail, A. G. B. Ahmad, Generalized c-distance in cone b-metric spaces and common fixed point results for weakly compatible self mappings, Int. J. Math. Anal., 9 (2015), 1593--1607
  • Google Scholar


• [17] Z. M. Fadail, A. G. B. Ahmad, Z. Golubovic, Fixed point theorems of single-valued mapping for c-distance in cone metric spaces, Abstr. Appl. Anal., 2012 (2012), 11 pages
  • View Article
  • MathSciNet


• [18] Z. M. Fadail, A. G. B. Ahmad, L. Paunovic, New fixed point results of single-valued mapping for c-distance in cone metric spaces, Abstr. Appl. Anal., 2012 (2012), 12 pages
  • View Article
  • MathSciNet


• [19] Z. M. Fadail, A. G. B. Ahmad, S. Radenovic, Common Fixed Point and Fixed Point Results under c-Distance in Cone Metric Spaces, Appl. Math. Inf. Sci. Lett., 1 (2013), 47--52
  • View Article
  • MathSciNet


• [20] Z. M. Fadail, A. G. B. Ahmad, S. Radenovic, M. Rajovic, On mixed g-monotone and w-compatible mappings in ordered cone b-metric spaces, Math. Sci., 9 (2015), 161--172
  • View Article
  • MathSciNet


• [21] K. Fallahi, M. Abbas, G. S. Rad, Generalized c-distance on cone b-metric spaces endowed with a graph and fixed point results, Appl. Gen. Topol., 18 (2017), 391--400
  • View Article
  • MathSciNet


• [22] A. A. Firozjah, H. Rahimi, M. De la Sen, G. S. Rad, Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras, Axioms, 9 (2020), 9 pages
  • View Article
  • Google Scholar


• [23] H. Huang, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl., 2013 (2013), 10 pages
  • MathSciNet
  • Google Scholar


• [24] L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468--1476
  • View Article
  • MathSciNet


• [25] S. Hussain, Fixed point and common fixed point theorems on ordered cone b-metric space over Banach algebra, J. Nonlinear Sci. Appl., 13 (2020), 22--33
  • View Article
  • MathSciNet


• [26] N. Hussain, M. H. Shah, KKM mappings in cone b-metric spaces, Comput. Math. Appl., 62 (2011), 1677--1684
  • View Article
  • MathSciNet


• [27] G. Jungck, S. Radenovic, S. Radojevic, V. Rakoevic, Common fixed point theorems for weakly compatible pairs on cone metric spaces, Fixed Point Theory Appl., 2009 (2009), 13 pages
  • View Article
  • MathSciNet


• [28] Z. Kadelburg, S. Radenovic, Coupled fixed point results under tvs-cone metric and w-cone-distance, Adv. Fixed Point Theory, 2 (2012), 29--46
  • View Article
  • Google Scholar


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


• [30] G. S. Rad, H. Rahimi, C. Vetro, Fixed point results under generalized c-distance with application to nonlinear fourth-order defferential equation, Fixed Point Theory, 20 (2019), 635--648
  • View Article
  • Google Scholar


• [31] H. Rahimi, S. Radenovic, G. S. Rad, P. Kumam, Quadrupled fixed point results in abstract metric spaces, Comput. Appl. Math., 33 (2014), 671--685
  • View Article
  • MathSciNet


• [32] N. Saleem, J. Vujakovic, W. U. Baloch, S. Radenovic, Coincidence point results for multivalued Suzuki type mappings using θ-contraction in b-metric spaces, Mathematics, 7 (2019), 1--21
  • View Article
  • Google Scholar


• [33] M. H. Shah, S. Simic, N. Hussain, A. Sretenovic, S. Radenovic, Common fixed points for occasionally weakly compatible pairs on cone metric type spaces, J. Comput. Anal. Appl.,, 14 (2012), 290--297
  • View Article
  • MathSciNet


• [34] W. Shatanawi, E. Karapınar, H. Aydi, Coupled coincidence points in partially ordered cone metric spaces with c-distance, J. Appl. Math., 2012 (2012), 15 pages
  • View Article
  • MathSciNet


• [35] W. Shatanawi, Z. D. Mitrovic, N. Hussain, S. Radenovic, On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras, Symmetry, 12 (2020), 12 pages
  • View Article
  • Google Scholar


• [36] L. Shi, S. Xu, Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 11 pages
  • View Article
  • MathSciNet


• [37] M. P. Stanic, A. S. Cvetkovic, S. Simic, S. Dimitrijevic, Common fixed point under contractive condition of Ciric’s type on cone metric type spaces, Fixed Point Theory Appl., 2012 (2012), 7 pages
  • View Article
  • MathSciNet


• [38] S. Wang, B. Guo, Distance in cone metric spaces and common fixed point theorems, Appl. Math. Lett., 24 (2011), 1735--1739
  • View Article
  • MathSciNet