Existence And Uniqueness Results For Delay Integral Equations In B-Metric Spaces

Abstract

This paper establishes a novel framework for analyzing nonlinear Volterra integral equations with hereditary effects within complete b-metric spaces. We investigate the existence and uniqueness of solutions to equations of the form:  under Lipschitz continuity and local boundedness conditions. Our approach introduces explicit a priori bounds and verifies operator continuity, constructing invariant sets where Agrawal's fixed-point theorem applies with computable constants satisfying . The theoretical advancements address significant limitations in global boundedness assumptions while maintaining verifiable convergence criteria. Practical applications to population dynamics and RLC circuits demonstrate the framework's efficacy, with explicit radius calculations ensuring consistency with hereditary system constraints.