A new characterization for Meir-Keeler condensing operators and its applications
Subject Areas : Statistics
H. Khandani
1
(Department of Mathematics, Mahabad Branch, Islamic Azad university, Mahabad, Iran)
F. Khojasteh
2
(Department of Mathematics, Arak Branch, Islamic Azad University, Arak, Iran.)
Keywords: عملگر های از نوع S, L-تابع, قضیه نقطه ثابت داربو, اندازه نافشردگی,
Abstract :
Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of them presented a characterization for Meir-Keeler condensing operators, which needs L-functions. But, finding an appropriate L-function needs more struggle. In this paper, we give a characterization for Meir-Keeler condensing operators via measure of non-compactness. Current characterization presents a criterion by which we can show that if a given generalization of Darbo's fixed point theorem is Meer-Keeler condensing or not. Ultimately, we give several corollaries and point out several generalizations of Darbo's fixed point theorem and show that all of them are Meir-Keeler condensing operator or a special case of this result.
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