Some extensions of Darbo's theorem and solutions of  integral equations of Hammerstein type

Allahyari, Reza; Aghajani, Asadollah

doi:10.22075/ijnaa.2017.1355.1334

Some extensions of Darbo's theorem and solutions of integral equations of Hammerstein type

Document Type : Research Paper

Authors

Reza Allahyari ¹

Asadollah Aghajani ²

¹ Department of Mathematics, Mashhad Branch, Islamic Azad University,mashhad, Iran

² School of Mathematics, Iran University of Science and Technology, Narmark, Tehran 16846 13114, Iran

10.22075/ijnaa.2017.1355.1334

Abstract

In this brief note, using the technique of measures of noncompactness, we give some extensions of Darbo fixed point theorem. Also we prove an existence result for a quadratic integral equation of Hammerstein type on an unbounded interval in two variables which includes several classes of nonlinear integral equations of Hammerstein type. Furthermore, an example is presented to show the efficiency of our result.

Keywords

Measure of noncompactness

Quadratic integral equation

Darbo fixed point theorem