On some properties of the solution set map to Volterra integral inclusion

Abstract

For the multivalued Volterra integral equation defined in a Banach space, the set of solutions is proved to be $R_\delta$, without auxiliary conditions imposed in Theorem 6 [J. Math. Anal. Appl. 403 (2013), 643-666]. It is shown that the solution set map, corresponding to this Volterra integral equation, possesses a continuous singlevalued selection; and the image of a~convex set under the solution set map is acyclic. The solution set to the Volterra integral inclusion in a separable Banach space and the preimage of this set through the Volterra integral operator are shown to be absolute retracts.