Contraction principles in \(M_s\)-metric spaces

Volume 10, Issue 2, pp 575--582 http://dx.doi.org/10.22436/jnsa.010.02.21

Publication Date: February 20, 2017 Submission Date: October 20, 2016

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)

• 2205 Downloads
• 3639 Views

Authors

N. Mlaiki - Department of Mathematical Sciences, Prince Sultan University. N. Souayah - Department of Natural Sciences, Community College, King Saud University. K. Abodayeh - Department of Mathematical Sciences, Prince Sultan University. T. Abdeljawad - Department of Mathematical Sciences, Prince Sultan University.

Abstract

In this paper, we give an interesting extension of the partial S-metric space which was introduced [N. Mlaiki, Univers. J. Math. Math. Appl., 5 (2014), 109–119] to the \(M_s\)-metric space. Also, we prove the existence and uniqueness of a fixed point for a self-mapping on an \(M_s\)-metric space under different contraction principles.

Share and Cite

Keywords

• Functional analysis
• \(M_s\)-metric space
• fixed point.

MSC

•  47H10
•  54H25

References

• [1] T. Abdeljawad, Fixed points for generalized weakly contractive mappings in partial metric spaces, Math. Comput. Modelling , 54 (2011), 2923–2927.
  • View Article
  • MathSciNet
  • Google Scholar


• [2] T. Abdeljawad, Meir-Keeler \(\alpha\)-contractive fixed and common fixed point theorems, Fixed Point Theory Appl., 2013 (2013 ), 10 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [3] T. Abdeljawad, H. Aydi, E. Karapınar , Coupled fixed points for Meir-Keeler contractions in ordered partial metric spaces, Math. Probl. Eng., 2012 (2012), 20 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [4] T. Abdeljawad, E. Karapınar, K. Taş, A generalized contraction principle with control functions on partial metric spaces, Comput. Math. Appl., 63 (2012), 716–719.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [5] I. Altun, A. Erduran, Fixed point theorems for monotone mappings on partial metric spaces, Fixed Point Theory Appl., 2011 (2011 ), 10 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] I. Altun, F. Sola, H. Simsek, Generalized contractions on partial metric spaces, Topology Appl., 157 (2010), 2778–2785.
  • Google Scholar


• [7] M. Asadi, E. Karapınar, P. Salimi, New extension of p-metric spaces with some fixed-point results on M-metric spaces, J. Inequal. Appl., 2014 (2014), 9 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [8] S. G. Matthews, Partial metric topology , Papers on general topology and applications, Flushing, NY, (1992), 183–197, Ann. New York Acad. Sci., 728 (1994),
  • View Article
  • MathSciNet
  • Google Scholar


• [9] N. Mlaiki, A contraction principle in partial S-metric spaces, Univers. J. Math. Math. Appl., 5 (2014), 109–119.
  • Google Scholar
  • MATH


• [10] N. Mlaiki, Common fixed points in complex S-metric space, Adv. Fixed Point Theory, 4 (2014), 509–524.


• [11] N. Mlaiki , \(\alpha-\psi\)-contractive mapping on S-metric space, Math. Sci. Lett., 4 (2015), 9–12.
  • View Article
  • Google Scholar


• [12] N. Mlaiki, A. Zarrad, N. Souayah, A. Mukheimer, T. Abdeljawad, Fixed point theorems in \(M_b\)-metric spaces, J. Math. Anal., 7 (2016), 1–9.
  • MATH


• [13] A. Shoaib, M. Arshad, J. Ahmad, Fixed point results of locally contractive mappings in ordered quasi-partial metric spaces, Sci. World J., 2013 (2013), 8 pages.
  • View Article
  • Google Scholar


• [14] S. Shukla, Partial b-metric spaces and fixed point theorems, Mediterr. J. Math., 11 (2014), 703–711.
  • View Article
  • Google Scholar


• [15] N. Souayah, A fixed point in partial \(S_b\)-metric spaces, An. St. Univ. Ovidius Constanţa, 24 (2016), 351–362.
  • View Article
  • MATH


• [16] N. Souayah, N. Mlaiki, A fixed point in \(S_b\)-metric spaces, J. Math. Comput. Sci., 16 (2016), 131–139.


• [17] O. Valero, On Banach fixed point theorems for partial metric spaces, Appl. Gen. Topol., 6 (2005), 229–240.
  • View Article
  • MathSciNet