Exploring α-ψ-ϕ contractive mapping: novel fixed point theorems in complete b-metric spaces.

Abstract

This paper explores the concept of $\alpha -\psi -\varphi$ contractive mappings, contributing to the advancement of self-map extensions and fixed-point theorems within b-metric spaces. We introduce a new class of contractive mappings and demonstrate how they extend traditional contraction principles, offering a broader framework for analyzing fixed points in non-standard spaces. The main result of this study is a generalization of existing fixed-point theorems, supported by comprehensive corollaries, illustrative examples, and rigorous proofs. These findings provide deeper insights into the structure of b-metric spaces and open avenues for further applications in fields such as optimization and machine learning.