On equivalence of generalized multi-valued contractions and Nadler's fixed point theorem

被引：24

作者：

Eldred, A. Anthony ^{[1
]}

Anuradha, J. ^{[1
]}

Veeramani, P. ^{[1
]}

机构：

[1] Indian Inst Technol, Dept Math, Madras, Tamil Nadu, India

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2007年 / 336卷 / 02期

关键词：

nadler's theorem; Generalized contraction; Reich's conjecture; Orbit of multi-valued map;

D O I：

10.1016/j.jmaa.2007.01.087

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We consider two generalizations of Nadler's theorem, one proved by Mizoguchi and Takahashi in response to the Reich conjecture and another theorem proved by Kaneko. We show that due to the additional conditions of these theorems the given multi-valued map reduces to a multi-valued contraction map. We prove this result by showing that the orbit of the multi-valued map is bounded under the contractive conditions of the two generalizations. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：751 / 757

页数：7

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