A New Existence Theorem of the Solution of a Functional Fredholm Integral Equation in b-metric Spaces

Abstract.

Using some recent results on nonlinear integral equations with new admissibility types in -metric spaces, this paper investigates the existence of solutions to a functional Fredholm integral equation in a -metric space. We establish the conditions under which a solution of the considered integral equation exists and then formulate an existence theorem for such solutions. This theorem complements the results obtained over time in the study of solutions to this type of functional Fredholm integral equation. The paper concludes with two illustrative examples that demonstrate the applicability of this existence theorem.