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

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Authors :

Latifa Benhamouche 1,3 and Smaïl Djebali 2.3

Author Address :

1 Department of Mathematics, Faculty of Sciences, BP 270. Blida, 09000. Algeria.
2 Department of Mathematics, Faculty of Sciences, Al Imam Mohammad Ibn Saud Islamic University (IMSIU), Saad Dahlab University, route de
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.



Article Info :

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



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