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

Rale M. Nikolić, Rajandra P. Pant, Vladimir T. Ristić and Aleksandar Šebeković
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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

Mathematics, 2022, vol. 10, issue 14, 1-11

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.

Keywords: probabilistic metric spaces; common fixed point; R -weakly commuting mappings; nonlinear contractive condition (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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