Remarks on two fixed-point theorems involving the sum and the product of two operators
β Scribed by B.C. Dhage
- Publisher
- Elsevier Science
- Year
- 2003
- Tongue
- English
- Weight
- 416 KB
- Volume
- 46
- Category
- Article
- ISSN
- 0898-1221
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β¦ Synopsis
In this article, we focus our attention on two fixed-point theorems of Krasnoselskii [l] and Dhage [2]. It is shown that some of the hypotheses of these fixed-point theorems are redundent. Our claim is also illustrated with an example.
π SIMILAR VOLUMES
## Abstract The purpose of this paper is to study the existence of fixed points for the sum of two nonlinear operators in the framework of real Banach spaces. Later on, we give some examples of applications of this type of results (Β© 2010 WILEYβVCH Verlag GmbH & Co. KGaA, Weinheim)
In the present paper, we prove some Krasnosel'skii-Leray-Schauder type fixed point theorems for weak topology. Some fixed point theorems for the sum of two weakly sequentially continuous mappings are also presented. Our results extend and improve on ones from several earlier works.
New easy proofs are given of the eigenvalue inequalities obtained by Amir-Moez for a product AB of two positive definite (strictly positive) operators A and B on a finite-dimensional Hilbert space. As a simple consequence of these inequalities, new bounds are established on the eigenvalues of AB whi