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September 10, 2025

Mappings with 𝒑-contraction, (𝝋, 𝚪,𝜷)-contraction on 𝒃- metric spaces and fixed point theorems

Key Points

The study establishes fixed point theorems for two types of contraction mappings in b-metric spaces.
It shows the uniqueness of solutions for the class of p-contraction and (𝜑, 𝛤, 𝛽)-contraction mappings.
The findings improve upon established concepts in existing literature, including applications beyond the Banach fixed point theorem.
Through examples, it illustrates cases where traditional fixed point theorems are not applicable, yet still supports the new results.

Abstract

The present study manifests some fixed point results focused on two type of contractive mappings in complete 𝑏-metric spaces. One is, the class of 𝑝-contraction with relate to a family of mappings and other is, (𝜑, 𝛤, 𝛽)-contraction mappings. Additionally, we prove uniqueness and a few fixed point theorems for these mentioned contractive mappings on 𝑏-metric spaces. These theorems make improvements and builds upon a number of well acknowledged concepts in a variety of current literature. To illustrate how the findings serve as suitable expansions of earlier results, an application is also given. A few examples from which the Banach fixed point theorem is not applicable are provided but these examples supports our findings. Therefore, the fixed point theorems from the existing literature are unified and generalized by our results.

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