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arXiv · 1812.02807

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

Radosław Pietkun
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Abstract

For the multivalued Volterra integral equation defined in a Banach space, the set of solutions is proved to be $R_δ$, 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. The image of a convex set under solution set map is acyclic. The solution set to 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.

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Radosław Pietkun. 2018-12-06. On the properties of the solution set map to Volterra integral inclusion. https://doi.org/10.12775/tmna.2017.006

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