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Journal of Applied Mathematics and Stochastic Analysis
Volume 6 (1993), Issue 3, Pages 261-269

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

University of the Aegean, Department of Mathematics, Karlovassi 83200, Samos, Greece

Received 1 August 1991; Revised 1 April 1993

Copyright © 1993 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In this paper we examine a class of nonlinear integral inclusions defined in a separable Banach space. For this class of inclusions of Volterra type we establish two existence results, one for inclusions with a convex-valued orientor field and the other for inclusions with nonconvex-valued orientor field. We present conditions guaranteeing that the multivalued map that represents the right-hand side of the inclusion is α-condensing using for the proof of our results a known fixed point theorem for α-condensing maps.