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

Abstract

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.

Keywords

• 47H10
• 45D05