New distance in cone \(S\)-metric spaces and common fixed point theorems

Volume 26, Issue 4, pp 368--378 http://dx.doi.org/10.22436/jmcs.026.04.05

Publication Date: January 06, 2022 Submission Date: August 14, 2021 Revision Date: November 05, 2021 Accteptance Date: November 29, 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)

• 991 Downloads
• 2480 Views

Authors

Z. M. Fadail - Department of Mathematics, Faculty of Education, Thamar University, 87246, Thamar, Republic of Yemen. A. Savic - School of Electrical and Computer Engineering, Academy of Technical and Art Applied Studies , Belgrade, Serbia. S. Radenovic - Faculty of Mechanical Engineering , University of Belgrade, Kraljice Marije 16, Belgrade, Serbia.

Abstract

In this work, we define a new distance called \(c_s\)-distance in a cone \(S\)-metric space with some properties. Then, we prove some common fixed point and fixed point theorems for self-mappings with this distance. After that, we obtain some common fixed point and fixed point results in the setting of cone \(S\)-metric spaces. We give some examples to support our work.

Share and Cite

Keywords

• Cone \(S\)-metric spaces
• \(c_s\)-distance
• common fixed points
• fixed points

MSC

•  47H10
•  54H25

References

• [1] S. Aleksic, Z. Kadelburg, Z. D. Mitrovic, S. Radenovc, A new survey: Cone metric spaces, J. Int. Math. Virtual Inst., 9 (2019), 93--121
  • View Article
  • MathSciNet


• [2] K. Anthony Singh, M. R. Singh, Some fixed point theorems of cone Sb-metric space, J. Indian Acad. Math., 40 (2018), 255--272
  • View Article


• [3] K. Anthony Singh, M. R. Singh, Some coupled fixed point theorems in cone Sb-metric space, J. Math. Comput. Sci., 10 (2020), 891--905
  • View Article
  • Google Scholar


• [4] D. Dhamodharan, R. Krishnakumar, Cone S-Metric Space and Fixed Point Theorems of Contractive Mappings, Ann. Pure Appl. Math., 14 (2017), 237--243
  • View Article
  • Google Scholar


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


• [6] J. K. Kim, S. Sedghi, N. Shobkolaei, Common fixed point theorems for the R-weakly commuting mappings in S-metric spaces, J. Comput. Anal. Appl., 19 (2015), 751--759
  • View Article
  • MathSciNet


• [7] N. Priyobarta, Y. Rohen, N. Mlaiki, Complex valued Sb-metric spaces, J. Math. Anal., 8 (2017), 13--24
  • View Article
  • Google Scholar


• [8] M. U. Rahman, M. Sarwar, Fixed point results of Altman integral type mappings in $S$-metric spaces, Int. J. Anal. Appl., 10 (2016), 58--63
  • View Article
  • Google Scholar


• [9] Y. Rohen, T. Došenović, S. Radenovic, A note on the paper "A fixed point theorem in $S_b$-metric spaces", Filomat, 31 (2017), 3335--3346
  • View Article
  • MathSciNet


• [10] G. S. Saluja, Fixed point theorems on cone S-metric spaces using implicit relation, CUBO, 22 (2020), 273--288
  • View Article
  • MathSciNet


• [11] G. S. Saluja, Some fixed point results under contractive type mappings in cone $S_b$-metric spaces, Palest. J. Math., 10 (2021), 547--561
  • View Article
  • MathSciNet


• [12] S. Sedghi, N. V. Dung, Fixed point theorems on $S$-metric space, Mat. Vesnik, 66 (2014), 113--124
  • View Article
  • MathSciNet


• [13] S. Sedghi, A. Gholidahneh, K. P. R. Rao, Common Fixed Point of Two R-Weakly Commuting Mappings in $S_b$-Metric Spaces, Math. Sci. Lett., 6 (2017), 249--253
  • View Article
  • Google Scholar


• [14] S. Sedghi, M. M. Rezaee, T. Došenović, S. Radenovic, Common fixed point theorems for contractive mappings satisfying $\Phi$-maps in $S$-metric spaces, Acta Univ. Sapientiae Math., 8 (2016), 298--311
  • View Article
  • MathSciNet


• [15] S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point in $S$-metric spaces, Mat. Vesnik, 64 (2012), 258--266
  • View Article
  • MathSciNet


• [16] S. Sedghi, N. Shobe, T. Došenovic, Fixed point results in $S$-metric spaces, Nonlinear Funct. Anal. Appl., 20 (2015), 55--67
  • Google Scholar


• [17] N. Souayah, N. Mlaiki, A fixed point theorem in Sb-metric spaces, J. Math. Computer Sci., 16 (2016), 131--139
  • View Article
  • Google Scholar


• [18] N. Tas, N.Özgür, New generalized fixed point results on $S_b$-metric spaces, Konuralp J. Math., 9 (2021), 24--32
  • View Article
  • MathSciNet


• [19] N. Van Dung, N. T. Hieu, S. Radojević, Fixed point theorems for $g$-monotone maps on partially ordered $S$-metric spaces, Filomat, 28 (2014), 1885--1898
  • View Article
  • MathSciNet


• [20] N. Yilmaz Özgür, N. Tas, Some fixed point theorems on $S$-metric spaces, Mat. Vesnik, 69 (2017), 39--52
  • View Article
  • MathSciNet