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

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

数学物理学报(英文版) ›› 2015, Vol. 35 ›› Issue (3): 552-566.doi: 10.1016/S0252-9602(15)30003-5

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

A. AGHAJANI¹, M. MURSALEEN², A. SHOLE HAGHIGHI³

1. School of Mathematics, Iran University of Science and Technology, Narmak, Iran;
2. Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, India;
3. Department of Mathematics, Karaj Branch, Islamic Azad University, Alborz, Iran

收稿日期:2013-05-07 修回日期:2014-06-30 出版日期:2015-05-01 发布日期:2015-05-01
通讯作者: A. AGHAJANI E-mail:aghajani@iust.ac.ir

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

A. AGHAJANI¹, M. MURSALEEN², A. SHOLE HAGHIGHI³

1. School of Mathematics, Iran University of Science and Technology, Narmak, Iran;
2. Department of Mathematics, Aligarh Muslim University, Aligarh-202 002, India;
3. Department of Mathematics, Karaj Branch, Islamic Azad University, Alborz, Iran

Received:2013-05-07 Revised:2014-06-30 Online:2015-05-01 Published:2015-05-01
Contact: A. AGHAJANI E-mail:aghajani@iust.ac.ir

摘要/Abstract

摘要：

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.

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

Abstract:

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

中图分类号:

47H09

A. AGHAJANI, M. MURSALEEN, A. SHOLE HAGHIGHI. FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS[J]. 数学物理学报(英文版), 2015, 35(3): 552-566.

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

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

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