Existence of solutions of $q$-functional integral equations with deviated argument

A. M. A. El-Sayed a,∗ Fatma. M. Gaafar b R. O. Abd-El-Rahman b and M. M. El-Haddad b

Existence of solutions of $q$-functional integral equations with deviated argument

Authors :

A. M. A. El-Sayed ^a,∗Fatma. M. Gaafar ^b R. O. Abd-El-Rahman ^b and M. M. El-Haddad^b

Author Address :

^aDepartment of Mathematics, Faculty of Science, Alexandria University, Alexandria, Egypt.
^bDepartment of Mathematics, Faculty of Science, Damanhour University, Damanhour, Egypt.

*Corresponding author.

Abstract :

In this paper, we study the existence of solutions for $q$-functional integral equations in Banach space~$C[0,T]$. The existence and uniqueness of solutions for the problems are proved by means of the Banach contraction principle.

Keywords :

$q$-functional integral equations; Banach contraction principle; Deviated argument; existence.

DOI :

Article Info :

Received : November 21, 2015; Accepted : January 15, 2016.