ON EXISTENCE THEOREMS FOR SOME NONLINEAR FUNCTIONAL-INTEGRAL EQUATIONS

In this paper, we present sufficient conditions for the existence of solutions of two different types of nonlinear functional-integral equations in Banach space C([0, a] x [0, b], R) consisting of real functions, defined and continuous on the set [0, a] x [0, b]. The main tools used in the proof are the concept of measures of noncompactness, Petryshyn fixed point theorem and Darbo's theorem in Banach space concerning the estimate on the solutions. Finally, we establish some examples of nonlinear functional -integral equations to show that our results are applicable.