Existence of strongly continuous solutions for a functional integral inclusion
Authors :
Ahmed M. A. El-Sayed a,∗ and Nesreen F. M. El-haddad b
Author Address :
a Department of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt.
b Department of Mathematics, Faculty of Science, Damanhour University, Egypt.
*Corresponding author.
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\[x(t) \in F(t, \int_{0}^{t}g(s,x(m(s)))ds),~~~t\in [0,T]\]
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.
DOI :
Article Info :
Received : January 25, 2017; Accepted : February 21, 2017.
