[Formula: see text]-Contraction in terms of measure of noncompactness with application for nonlinear integral equations

Farzaneh Nikbakhtsarvestani; S Mansour Vaezpour; Mehdi Asadi

doi:10.1186/s13660-017-1545-2

[Formula: see text]-Contraction in terms of measure of noncompactness with application for nonlinear integral equations

J Inequal Appl. 2017;2017(1):271. doi: 10.1186/s13660-017-1545-2. Epub 2017 Oct 30.

Authors

Farzaneh Nikbakhtsarvestani¹, S Mansour Vaezpour², Mehdi Asadi³

Affiliations

¹ Young Researchers and Elite club, Shiraz Branch, Islamic Azad University, Shiraz, Iran.
² Department of Mathematics and Computer Sciences, Amirkabir University of Technology, Tehran, Iran.
³ Department of Mathematics, Zanjan Branch, Islamic Azad University, Zanjan, Iran.

Abstract

In this paper, some new generalization of Darbo's fixed point theorem is proved by using a [Formula: see text]-contraction in terms of a measure of noncompactness. Our result extends to obtaining a common fixed point for a pair of compatible mappings. The paper contains an application for nonlinear integral equations as well.

Keywords: [Formula: see text]-contraction; fixed point; measure of noncompactness.