Electron. J. Diff. Equ., Vol. 2012 (2012), No. 137, pp. 1-12.

Existence of solutions for mixed Volterra-Fredholm integral equations

Asadollah Aghajani, Yaghoub Jalilian, Kishin Sadarangani

In this article, we give some results concerning the continuity of the nonlinear Volterra and Fredholm integral operators on the space $L^{1}[0,\infty)$. Then by using the concept of measure of weak noncompactness, we prove an existence result for a functional integral equation which includes several classes of nonlinear integral equations. Our results extend some previous works.

Submitted May 11, 2012. Published August 19, 2012.
Math Subject Classifications: 45G10, 47H08.
Key Words: Functional integral equation; fixed-point; Nemytski operator; measure of weak noncompactness; Caratheodory conditions.

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Asadollah Aghajani
School of Mathematics
Iran University of Science and Technology
Narmak, Tehran 16846-13114, Iran
email: aghajani@iust.ac.ir
Yaghoub Jalilian
Department of Mathematics
Razi University
Kermanshah 67149, Iran
email: yajalilian@iust.ac.ir
Kishin Sadarangani
Department of Mathematics
University of Las Palmas de Gran Canaria
35017 Las Palmas de Gran Canaria, Spain
email: ksadaran@dma.ulpgc.es

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