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Русская версия

**A.M.A. El-Sayed**

Faculty of Science,

Alexandria University,

Alexandria,

Egypt

**R. O. Abd El Rahman**

Faculty of Science,

Damanhour University,

Behera, Egypt

**Fatma F. M. Gaffar**

Faculty of Science,

Damanhour University,

Behera, Egypt

**Nesreen El-Haddad**

Faculty of Science,

Damanhour University,

Behera, Egypt

The existence of weak solutions of integral equations and some coupled systems of integral equations have been studied, on some suitable assumptions, by some authors. In this work we concern with a coupled system of nonlinear Volterra-Urysohn functional integral equations in the reflexive Banach space E. The existence of weakly continuous solutions, in the Banach space C[I,E], will be proved under some certain assumptions concerning the functional equations that under the integral sign. As an application, the coupled system of nonlinear Volterra-Hammerstien functional integral equations is also studied.

- Coupled system
- Fixed point theorem
- Functional integral equations
- Weak solutions

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