Measure of noncompactness on Lp(RN) and applications

A. Aghajani; D. O'Regan; A. Shole Haghighi

doi:10.4067/S0719-06462015000100007

Authors

A. Aghajani School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844-13114, Iran.
D. O'Regan School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland. Nonlinear Analysis and Applied Mathematics (NAAM), Department of Mathematics, King Abdulaziz University, Jeddah, Saudi Arabia.
A. Shole Haghighi School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16844-13114, Iran.

DOI:

https://doi.org/10.4067/S0719-06462015000100007

Keywords:

Measure of noncompactness, Darbo‘s fixed point theorem, Fixed point

Abstract

In this paper we define a new measure of noncompactness on L^p(IR^N) (1 â‰¤ p < âˆž) and study its properties. As an application we study the existence of solutions for a class of nonlinear functional integral equations using Darbo‘s fixed point theorem associated with this new measure of noncompactness.