On quadratic integral equations of Volterra type  in  Fr’echet spaces

Latifa Benhamouche 1,3 and Smaïl Djebali 2.3

doi:10.26637/MJM0604/0007

On quadratic integral equations of Volterra type in Fr’echet spaces

Authors :

Latifa Benhamouche ^1,3 and Smaïl Djebali ^2.3

Author Address :

¹ Department of Mathematics, Faculty of Sciences, BP 270. Blida, 09000. Algeria.
²Department of Mathematics, Faculty of Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Saad Dahlab University, route de
Soumaa.
³ Laboratoire "Théorie du Point Fixe et Applications", ENS, BP 92 Kouba. Algiers, 16006. Algeria.

*Corresponding author.

Abstract :

In this work, we investigate the existence of solutions to a quadratic integral equation of Volterra type. By using the Schauder Tychonoff fixed point theorem in $C(Omega,mathbb{R})$, the Fr’echet Space of real continuous functions on unbounded open subset $Omegasubsetmathbb{R}^n$, we establish the existence of at least one solution.

Keywords :

Quadratic integral equation, Schauder-Tychonoff fixed point theorem, Volterra operator, Fr’echet space.

DOI :

10.26637/MJM0604/0007

Article Info :

Received : April 11, 2018; Accepted : September 29, 2018.