EXISTENCE THEOREMS FOR GENERALIZED NONLINEAR PERTURBED ABSTRACT MEASURE INTEGRODIFFERENTIAL EQUATIONS

In this paper, we prove the relevance and local existence theorems for a class of generalized nonlinear perturbed abstract measure integrodifferential equations via classical hybrid fixed point theorems of Dhage (1992,2003) under mixed weaker Lipschitz and Caratheodory conditions. The existence of extremal solutions is obtained between the given lower and upper solutions under certain monotonicity conditions. Our natural hypotheses and claims have also been illustrated with a couple of numerical examples.