Existence of Solutions to Symmetric Multivalued Functional Integral Equations with Illustrative Applications in Medicine and Logistics

This paper investigates functional integral equations with multivalued terms that appear symmetrically on both sides of the equation. We impose structural conditions on the coefficients that, while insufficient to ensure uniqueness, are adequate to guarantee the existence of at least one solution. We assumed mere continuity of the coefficients to establish a Peano-type existence theorem. The existence result was derived through the application of Schauder’s fixed-point theorem. We further highlighted that this finding for symmetric multivalued functional integral equations significantly informs the analysis of delayed multivalued functional equations, which is commonly utilized in modeling processes where both the present and past states of the system play a crucial role. To illustrate the applicability of the proposed frameworks, representative examples were formulated and numerically solved for each type of equation, highlighting potential use cases in medicine and logistics.