Probabilistic extension of a general fixed point theorem

Vladimir T. Ristić; R. P. Pant; Rale M. Nikolić

doi:10.2298/FIL2510343R

Probabilistic extension of a general fixed point theorem

Vladimir T. Ristić, R. P. Pant, Rale M. Nikolić

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

Abstract

As a probabilistic extension of the theorem obtained by Pant et al. [R.P. Pant, V. Rakočević, D. Gopal, A. Pant, M. Ram, A General Fixed Point Theorem, Filomat 35(12) (2021), 4061–4072] in this paper, we prove existence and uniqueness of a fixed point for a wide class of self-mapping defined on complete Menger PM-space. Our theorem generalizes well-known fixed point theorems proved for Menger PM spaces. Also, this theorem characterizes probabilistic metric completeness. Some examples and comments are provided based on the obtained results.

Original language	English
Pages (from-to)	3343-3352
Number of pages	10
Journal	Filomat
Volume	39
Issue number	10
DOIs	https://doi.org/10.2298/FIL2510343R
Publication status	Published - 2025
Externally published	Yes

Keywords

Contractive mapping
Fixed point
Menger PM-spaces
Weak orbital continuity

ASJC Scopus subject areas

General Mathematics

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10.2298/FIL2510343R

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title = "Probabilistic extension of a general fixed point theorem",

abstract = "As a probabilistic extension of the theorem obtained by Pant et al. [R.P. Pant, V. Rako{\v c}evi{\'c}, D. Gopal, A. Pant, M. Ram, A General Fixed Point Theorem, Filomat 35(12) (2021), 4061–4072] in this paper, we prove existence and uniqueness of a fixed point for a wide class of self-mapping defined on complete Menger PM-space. Our theorem generalizes well-known fixed point theorems proved for Menger PM spaces. Also, this theorem characterizes probabilistic metric completeness. Some examples and comments are provided based on the obtained results.",

keywords = "Contractive mapping, Fixed point, Menger PM-spaces, Weak orbital continuity",

author = "Risti{\'c}, {Vladimir T.} and Pant, {R. P.} and Nikoli{\'c}, {Rale M.}",

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doi = "10.2298/FIL2510343R",

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T1 - Probabilistic extension of a general fixed point theorem

AU - Ristić, Vladimir T.

AU - Pant, R. P.

AU - Nikolić, Rale M.

PY - 2025

Y1 - 2025

N2 - As a probabilistic extension of the theorem obtained by Pant et al. [R.P. Pant, V. Rakočević, D. Gopal, A. Pant, M. Ram, A General Fixed Point Theorem, Filomat 35(12) (2021), 4061–4072] in this paper, we prove existence and uniqueness of a fixed point for a wide class of self-mapping defined on complete Menger PM-space. Our theorem generalizes well-known fixed point theorems proved for Menger PM spaces. Also, this theorem characterizes probabilistic metric completeness. Some examples and comments are provided based on the obtained results.

AB - As a probabilistic extension of the theorem obtained by Pant et al. [R.P. Pant, V. Rakočević, D. Gopal, A. Pant, M. Ram, A General Fixed Point Theorem, Filomat 35(12) (2021), 4061–4072] in this paper, we prove existence and uniqueness of a fixed point for a wide class of self-mapping defined on complete Menger PM-space. Our theorem generalizes well-known fixed point theorems proved for Menger PM spaces. Also, this theorem characterizes probabilistic metric completeness. Some examples and comments are provided based on the obtained results.

KW - Contractive mapping

KW - Fixed point

KW - Menger PM-spaces

KW - Weak orbital continuity

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SP - 3343

EP - 3352

JO - Filomat

JF - Filomat

IS - 10

ER -

Probabilistic extension of a general fixed point theorem

Abstract

Keywords

ASJC Scopus subject areas

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