6th International Young Scientist Congress (IYSC-2020) will be Postponed to 8th and 9th May 2021 Due to COVID-19. 10th International Science Congress (ISC-2020).  International E-publication: Publish Projects, Dissertation, Theses, Books, Souvenir, Conference Proceeding with ISBN.  International E-Bulletin: Information/News regarding: Academics and Research

A new fixed point theorem in modular metric spaces

Author Affiliations

  • 1Bhilai institute of technology, Bhilai, India

Res. J. Mathematical & Statistical Sci., Volume 8, Issue (2), Pages 17-20, May,12 (2020)


In this article, a brief introduction of Modular metric spaces with some fixed point theorems are given from the modular theory of Chistyakov. After that some new concepts are discussed, which are related with the existence of fixed point from the Reich contraction mapping in the modular metric spaces.


  1. Nakano, H., (1950)., Modulared semi-ordered linear spaces., In Tokyo Math. Bookser., 1, Marcezen Co., Tokyo.
  2. Musielak, J. and Orlicz, W. (1959)., On modular spaces., Studia Math., 18(1), 49-65.
  3. Khamsi, M.A, Koziowski, W.K. and Reich, S. (1990)., Fixed point theory in modular function spaces., Nonlinear Anal., 14(11), 935-953.
  4. Chistyakov, V.V. (2006)., Metric modular and their application., Akad. Nauk, 406(2), 165-168.
  5. Chistyakov, V.V. (2008)., Modular metric spaces generated by F- modular., Folia Math, 15(1), 3-24.
  6. Chistyakov, V.V. (2010)., Modular metric spaces I: basic concepts., Nonlinear Anal., 72(1), 1-14.
  7. Chistyakov, V.V. (2010)., Modular metric spaces, II: application to superposition operators. Nonlinear Analysis: Theory, Methods & Applications, 72(1), 15-30., undefined
  8. Abdou, A. A., & Khamsi, M. A. (2013)., Fixed point results of point wise contractions in modular metric spaces., Fixed Point Theory & Applications, 2013(1), 163.
  9. Khamsi, M. A. (1996)., A convexity property in modular function spaces., Mathematica Japonica, 44, 269-280.
  10. Kozlowski, W.M., (1988)., Modular function spaces, monographs and Text books in pure and applied mathematics., 122, Marcel Dekker, Inc., New York .
  11. Jleli, M., & Samet, B. (2015)., A generalized metric space and related fixed point theorems., Fixed point theory and Applications, (61)2015, 1-14.
  12. Abdou, A. A., & Khamsi, M. A. (2014)., Fixed points of multivalued contraction mappings in modular metric spaces., Fixed Point Theory & Applications, 2014(1), 249.