The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
권호 표지
DOI QR코드

DOI QR Code

COMMON FIXED POINT RESULTS ON FUZZY METRIC SPACES AND MODULAR METRIC SPACES VIA SIMULATION FUNCTION

  • Received : 2019.11.22
  • Accepted : 2020.02.25
  • Published : 2020.05.31
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we prove common fixed point theorems for two mappings by using simulation function on fuzzy metric spaces. We also deduce some consequences in modular metric spaces.

Keywords

References

  1. 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.
  2. V.V. Chistyakov: Modular metric spaces, I Basic concepts. Nonlinear Anal. 72 (2010), 1-14. https://doi.org/10.1016/j.na.2009.04.057
  3. V.V. Chistyakov: Modular metric spaces, II Application to superposition operators. Nonlinear Anal. 72 (2010), 15-30. https://doi.org/10.1016/j.na.2009.04.018
  4. M. Demma, R. Saadati & P. Vetro: Fixed point results on b- metric space via picard sequences and b- simulation functions. Iranian J. Math. Sci. Infor. 11 (2016), 123-136.
  5. A. George & P. Veeramani: On some results in fuzzy metric spaces. Fuzzy Sets and Systems 64 (1994), 395-399. https://doi.org/10.1016/0165-0114(94)90162-7
  6. N. Hussain & P. Salimi: Implicit contractive mappings in modular metric and fuzzy metric spaces. Scientific Word J., 2014, 12 pages.
  7. F. Khojasteh, S. Shukla & S. Radenovic: A new approach to the study of fixed point theory via simulation functions. Filomat. 29 (2015), 1189-1194. https://doi.org/10.2298/FIL1506189K
  8. O. Kramosil & J. Michalek: Fuzzy metric and statistical metric spaces. Kybernetica 11 (1975), 336-344.
  9. A. Nastasi & P. Vetro: Fixed point results on metric and partial metric spaces via simulation functions. J. Nonlinear Sci. Appl. 8 (2015), 1059-1069. https://doi.org/10.22436/jnsa.008.06.16
  10. A. Nastasi & P. Vetro: Existence and uniqueness for a first order periodic differential problem via fixed point results. Results Mth. 71 (2017), 889-909. https://doi.org/10.1007/s00025-016-0551-x
  11. A.F. Roldan-Lopez-de-Hierro, E. Karapinar, C. Roldan-Lopex-de-Hierro & J. Martinez-Moreno: Coincidence point theorems on metric spaces via simulation functions. J. Comput. Appl. Math. 275 (2015), 345-355. https://doi.org/10.1016/j.cam.2014.07.011
  12. B. Schweizer & A. Sklar: Statistical spaces. Pacific J. Math 10 (1960), 189-205.
  13. S. Radenovic, F. Vetro & J. Vujakovic: An alternative and easy approach to fixed point results via simulation functions. Demonstr. Math 50 (2017), 223-230. https://doi.org/10.1515/dema-2017-0022
  14. Y. Tanaka, Y. Mizuno & T. Kado: Chaotic dynamics in the Friedmann equation. Chaos, Solitons and Fractals 24 (2005), no. 2, 407-422. https://doi.org/10.1016/j.chaos.2004.09.034
  15. F. Tchier, C. Vetro & F. Vetro: Best approximation and variational inequality problems involving a simulation function. Fixed Point Theory Appl. 2016, 2016:26.