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

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

doi:10.3390/math10142449

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

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

Mathematics and Applied Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

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 (Formula presented.) (or type (Formula presented.)). These results generalize some known results.

Original language	English
Article number	2449
Journal	Mathematics
Volume	10
Issue number	14
DOIs	https://doi.org/10.3390/math10142449
Publication status	Published - Jul 2022

Keywords

R-weakly commuting mappings
common fixed point
nonlinear contractive condition
probabilistic metric spaces

ASJC Scopus subject areas

Computer Science (miscellaneous)
General Mathematics
Engineering (miscellaneous)

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10.3390/math10142449

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title = "Common Fixed Points Theorems for Self-Mappings in Menger PM-Spaces",

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 (Formula presented.) (or type (Formula presented.)). These results generalize some known results.",

keywords = "R-weakly commuting mappings, common fixed point, nonlinear contractive condition, probabilistic metric spaces",

author = "Nikoli{\'c}, {Rale M.} and Pant, {Rajandra P.} and Risti{\'c}, {Vladimir T.} and Aleksandar {\v S}ebekovi{\'c}",

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AU - Ristić, Vladimir T.

AU - Šebeković, Aleksandar

PY - 2022/7

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AB - 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 (Formula presented.) (or type (Formula presented.)). These results generalize some known results.

KW - R-weakly commuting mappings

KW - common fixed point

KW - nonlinear contractive condition

KW - probabilistic metric spaces

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

Abstract

Keywords

ASJC Scopus subject areas

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