Existence and Uniqueness Results for the Solution of Interval Fredholm Integral Equations via Fixed-Point Theorem Under a Parametric Framework

This study investigates the conditions for the existence and uniqueness of solutions to interval Fredholm integral equations (IFIEs). To achieve this objective, a metric is introduced on the space of continuous parameterized interval-valued functions (IV-functions) defined over a compact interval. Preliminary concepts, including self-mappings, contraction mappings on this function space and the fixed-point theorem are discussed to establish the theoretical foundation. The standard formulation of IFIEs is then presented. Utilizing the contraction mapping principle and the associated fixed-point theorem, sufficient conditions ensuring the existence and uniqueness of solutions to IFIEs are derived, constituting the primary contribution of this work. Finally, a systematic solution procedure for IFIEs is outlined and illustrated through numerical examples.