Common fixed point of four maps in Sm-metric space

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K. Mallaiah
V. Srinivas

Abstract

In this paper, first, we deal with new metric space Sm-metric space that combines multiplicative metric space and S-metric space. We generate a common fixed point theorem in a Sm-metric space using the notions of reciprocally continuous mappings, faintly compatible mappings and occasionally weakly compatible mappings (OWC). We are also studying the well-posedness of Sm metric space. Further, some examples are presented to support our outcome.

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References

  1. A.E. Bashirov, E.M. Kurpınar, A. Ozyapıcı, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (2008), 36–48.
  2. M. Ozav¸sar, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, J. Eng. Technol. Appl. Sci. 2 (2017), 65–79.
  3. V. Srinivas, K. Mallaiah, Some results on weaker class of compatible mappings in S-metric space, Malaya J. Mat. 8 (2020), 1132-1137.
  4. V. Srinivas, K. Satyanna. Some results in Mnrger space by using sub compatible, faintly compatible mappings, Malaya J, Mat. 9 (2021), 725-730.
  5. S. Sedghi, N. Shobkolaei, M. Shahraki, T. Dosenovic, Common fixed point of four maps in S-metric spaces, Math. Sci. 12 (2018), 137–143.
  6. R.P. Pant, Common fixed points of four mappings, Bull. Cal. Math. Soc. 90 (1998), 281–286.
  7. V. Naga Raju Some properties of multiplicative s-metric spaces, Adv. Math.: Sci. J. 10 (2021), 105–109.
  8. G. Jungck, B.E Rhoades, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29 (1998), 227-238.
  9. M.A. Al-Thagafi, N. Shahzad Generalized -non expansive self maps and invariant approximations Acta Math. Sin. (Engl. Ser.), 24 (2008), 867-876.
  10. R.K. Bisht, N. Shahzad, Faintly compatible mappings and common fixed points, Fixed Point Theory Appl. 2013 (2013), 156.
  11. F.S. de Blasi, J. Myjak, Sur la porosite de l’ensemble des contractions sans point fixe. C. R. Acad. Sci. Paris 308 (1989), 51–54.