On the existence of solutions for Volterra integral inclusions in Banach spaces (Q1315888)

A class of nonlinear integral inclusions defined in a separable Banach space is examined. For this class of inclusions of Volterra type two existence results are established: one for inclusions with a convex- valued orientor field and the other for inclusions with nonconvex-valued orientor field. Conditions are presented guaranteeing that the multi- valued map that represents the right hand side of the inclusion is \(\alpha\)-condensing using for the proof of the given results a known fixed point theorem for \(\alpha\)-condensing maps.