FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

doi:10.1016/S0252-9602(15)30003-5

Abstract

Abstract:

In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.

Key words: Measure of noncompactness, Darbo fixed point theorem, couple fixed point, Meir-Keeler condensing operator, Volterra integral equation

CLC Number:

47H09

A. AGHAJANI, M. MURSALEEN, A. SHOLE HAGHIGHI. FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS[J].Acta mathematica scientia,Series B, 2015, 35(3): 552-566.

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