Existence of strongly continuous solutions for a functional integral inclusion

Ahmed M. A. El-Sayed; Nesreen F. M. El-haddad

doi:10.26637/mjm502/022

Abstract

In this paper we are concerned with the existence of strongly continuous solution $x \in C[I, E]$ of the nonlinear functional integral inclusion
$$
x(t) \in F\left(t, \int_0^t g(s, x(m(s))) d s\right), \quad t \in[0, T]
$$
under the assumption that the set-valued function $F$ has Lipschitz selection in the Banach space $E$.

Keywords:

Set-valued function, continuous solutions, Functional integral inclusions, selections of the set-valued function, Lipschitz selections

Mathematics Subject Classification:

Mathematics

Authors Imprint References Funding Related Articles Downloads

Ahmed M. A. El-Sayed Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt. https://orcid.org/0000-0001-7092-7950
Nesreen F. M. El-haddad Department of Mathematics, Faculty of Science, Damanhour University, Egypt.

Pages: 442-448
Date Published: 01-04-2017
Vol. 5 No. 02 (2017): Malaya Journal of Matematik (MJM)

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