Fixed point theorem by using ψ–contraction and (ϕ,φ)–contraction in probabilistic 2–metric spaces

This research paper investigates and proves some theorems of the fixed point for self–mapping [T:X→X] under (ϕ,ψ)–contractive mappings and (ϕ,φ)–contractive mappings in Menger probabilistic 2–metric space. These theorems are used as an essential tool to convert the probabilistic metric to 2–metric s...

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Bibliographic Details
Published in:Alexandria engineering journal 2020-06, Vol.59 (3), p.1239-1242
Main Authors: Abu-Donia, H.M., Atia, H.A., Khater, Omnia M.A.
Format: Article
Language:English
Subjects:
2–metric Space
45D05
47H10
[formula omitted]–contractive mapping
Fixed point
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Summary:This research paper investigates and proves some theorems of the fixed point for self–mapping [T:X→X] under (ϕ,ψ)–contractive mappings and (ϕ,φ)–contractive mappings in Menger probabilistic 2–metric space. These theorems are used as an essential tool to convert the probabilistic metric to 2–metric space and are employed to prove the uniqueness and existence the fixed point of the a mapping T from a complete 2–Menger probabilistic space into itself. The used definitions and theorems show effective and possibility of our main idea.
ISSN:1110-0168
DOI:10.1016/j.aej.2020.02.009