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September 5, 2025Journal of Mathematics0 citationsOpen Access

On Some Fixed‐Point Results in Cone Ab‐Metric Space Over a Real Banach Algebra Without the Assumption of Normality of Cone

KSKumam Anthony SinghManipur University KDKaruna DeviIndian Veterinary Research Institute KDKamalini DeviNational Institute of Technology Warangal

Key Points

The research highlights fixed-point results in cone metric spaces that do not require normality assumptions.
New theorems extend classical results from Banach, Chatterjea, and Kannan types, broadening their applicability.
An example demonstrates the results, reinforcing their validity in practical contexts.
The study also establishes the existence of a unique solution for nonlinear Fredholm integral equations.

Abstract

In this paper, we introduce the concept of cone A b ‐metric space over real Banach algebra and prove some fixed‐point theorems of the Banach, Chatterjea, and Kannan types in such space without assuming normality of the cone. Our results extend and generalize many previously known results in the existing literature. An example is given to support our results. We also apply our result to examine the existence of unique solution for a nonlinear Fredholm integral equation.

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