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.
Citation
Radosław Pietkun. "On some properties of the solution set map to Volterra integral inclusion." Topol. Methods Nonlinear Anal. 49 (2) 715 - 737, 2017. https://doi.org/10.12775/TMNA.2017.006
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