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

Area of Science:

• Mathematical Analysis
• Topology

Background:

• Fixed-point theory is crucial for solving equations in various mathematical fields.
• B-metric spaces offer a generalized framework beyond traditional metric spaces.
• Existing contractive mappings have limitations in certain non-standard spaces.

Purpose of the Study:

• To introduce and investigate a novel class of contractive mappings.
• To extend existing fixed-point theorems within the context of b-metric spaces.
• To provide a more comprehensive framework for analyzing self-maps and fixed points.

Main Methods:

• Definition of a new class of contractive mappings tailored for b-metric spaces.
• Development of generalized fixed-point theorems based on these new mappings.
• Rigorous mathematical proofs, corollaries, and illustrative examples to support the theorems.

Main Results:

• A new class of contractive mappings is successfully defined and analyzed.
• Generalization of existing fixed-point theorems in b-metric spaces is achieved.
• The study provides a broader theoretical foundation for fixed-point analysis.

Conclusions:

• The introduced contractive mappings offer enhanced capabilities for fixed-point theorems.
• Findings deepen the understanding of b-metric spaces and their properties.
• Potential applications are identified in optimization, machine learning, and other areas.