An Implicit Hybrid Delay Functional Integral Equation: Existence of Integrable Solutions and Continuous Dependence

Abstract

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.

Keywords

• measure of noncompactness
• darbo fixed point theorem
• monotonic integrable solutions
• uniqueness of the solution
• continuous dependence of solution