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Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces

Author

Listed:
  • Rale M. Nikolić

    (Department of Natural Sciences and Mathematics, Military Academy, University of Defence, Pavla Jurišića Šturma 33, 11105 Belgrade, Serbia)

  • Rajandra P. Pant

    (Dalhausie Villa Compound, Ayarpata, Mallital, Nainital 263001, India)

  • Vladimir T. Ristić

    (Faculty of Education, University in Kragujevac, Milana Mijalkovića 14, 35000 Jagodina, Serbia)

  • Aleksandar Šebeković

    (State University of Novi Pazar, Vuka Karadžića bb, 36300 Novi Pazar, Serbia)

Abstract

The purpose of this paper is to prove that orbital continuity for a pair of self-mappings is a necessary and sufficient condition for the existence and uniqueness of a common fixed point for these mappings defined on Menger PM-spaces with a nonlinear contractive condition. The main results are obtained using the notion of R -weakly commutativity of type A f (or type A g ). These results generalize some known results.

Suggested Citation

  • Rale M. Nikolić & Rajandra P. Pant & Vladimir T. Ristić & Aleksandar Šebeković, 2022. "Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces," Mathematics, MDPI, vol. 10(14), pages 1-11, July.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:14:p:2449-:d:862122
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    References listed on IDEAS

    as
    1. Gopal, Dhananjay & Abbas, Mujahid & Vetro, Calogero, 2014. "Some new fixed point theorems in Menger PM-spaces with application to Volterra type integral equation," Applied Mathematics and Computation, Elsevier, vol. 232(C), pages 955-967.
    2. Gerald Jungck, 1986. "Compatible mappings and common fixed points," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 9, pages 1-9, January.
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