From fuzzy metric spaces to modular metric spaces: a fixed point approach

Volume 10, Issue 2, pp 451--464 http://dx.doi.org/10.22436/jnsa.010.02.11

Publication Date: February 20, 2017 Submission Date: November 07, 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)

• 2248 Downloads
• 3711 Views

Authors

Fairouz Tchier - Mathematics Department, College of Science (Malaz), King Saud University, P. O. Box 22452, Riyadh, King Saudi Arabia. Calogero Vetro - Department of Mathematics and Computer Science, University of Palermo, Via Archirafi 34, 90123, Palermo, Italy. Francesca Vetro - Department of Energy, Information Engineering and Mathematical Models (DEIM), University of Palermo, Viale delle Scienze, 90128, Palermo, Italy.

Abstract

We propose an intuitive theorem which uses some concepts of auxiliary functions for establishing existence and uniqueness of the fixed point of a self-mapping. First we work in the setting of fuzzy metric spaces in the sense of George and Veeramani, then we deduce some consequences in modular metric spaces. Finally, a sample homotopy result is derived making use of the main theorem.

Share and Cite

Keywords

• Fixed point
• fuzzy metric space
• modular metric space.

MSC

•  54H25
•  54A40

References

• [1] A. A. N. Abdou, M. A. Khamsi, Fixed point results of pointwise contractions in modular metric spaces, Fixed Point Theory Appl., 2013 (2013 ), 11 pages.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [2] R. P. Agarwal, M. Meehan, D. O’Regan , Fixed point theory and applications, Cambridge Tracts in Mathematics, Cambridge University Press, Cambridge (2002)
  • Google Scholar


• [3] H. Argoubi, B. Samet, C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl., 8 (2015), 1082–1094.
  • MathSciNet
  • Google Scholar
  • MATH


• [4] B. Azadifar, G. Sadeghi, R. Saadati, C.-K. Park, Integral type contractions in modular metric spaces, J. Inequal. Appl., 2013 (2013), 14 pages.
  • View Article
  • MathSciNet
  • Google Scholar


• [5] V. V. Chistyakov , Modular metric spaces, I, Basic concepts, Nonlinear Anal., 72 (2010), 1–14.
  • View Article
  • MathSciNet
  • Google Scholar


• [6] V. V. Chistyakov, Modular metric spaces,II, Application to superposition operators, Nonlinear Anal., 72 (2010), 15–30.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [7] C. Di Bari, C. Vetro, Fixed points, attractors and weak fuzzy contractive mappings in a fuzzy metric space, J. Fuzzy Math., 13 (2005), 973–982.
  • MathSciNet
  • Google Scholar
  • MATH


• [8] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Sets and Systems, 64 (1994), 395–399.
  • View Article
  • Google Scholar


• [9] V. Gregori, A. López-Crevillén, S. Morillas, A. Sapena, On convergence in fuzzy metric spaces, Topology Appl., 156 (2009), 3002–3006.
  • View Article
  • Google Scholar


• [10] V. Gregori, S. Morillas, A. Sapena, On a class of completable fuzzy metric spaces, Fuzzy Sets and Systems, 161 (2010), 2193–2205.
  • View Article
  • MathSciNet
  • Google Scholar
  • MATH


• [11] V. Gregori, S. Romaguera, On completion of fuzzy metric spaces, Theme: Fuzzy intervals, Fuzzy Sets and Systems, 130 (2002), 399–404.
  • View Article
  • Google Scholar


• [12] N. Hussain, P. Salimi , Implicit contractive mappings in modular metric and fuzzy metric spaces, Scientific World J., 2014 (2014), 12 pages.
  • View Article
  • Google Scholar


• [13] F. Khojasteh, S. Shukla, S. Radenović, A new approach to the study of fixed point theory for simulation functions, Filomat, 29 (2015), 1189–1194.
  • View Article
  • MathSciNet
  • MATH


• [14] D. Mihet, On fuzzy contractive mappings in fuzzy metric spaces, Fuzzy Sets and Systems, 158 (2007), 915–921.
  • View Article
  • Google Scholar


• [15] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (1965), 338–353.