APPROXIMATION, EXISTENCE AND UNIQUENESS OF THE INTEGRABLE LOCAL SOLUTION OF NONLINEAR HYBRID FUNCTIONAL INTEGRAL EQUATIONS

In this paper, we prove a couple of approximation results for existence and uniqueness of the integrable local solutions of nonhomogeneous nonlinear hybrid functional integral equations under weaker partial compactness, partial Lipschitz and usual monotonicity type conditions. We employ the Dhage monotone iteration method based on the recent hybrid fixed point theorems of Dhage (2024) while establishing our main results of this paper. Our hypotheses and abstract results are also illustrated with a couple of numerical examples.