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Remarks on Separation of Convex Sets, Fixed-Point Theorem, and Applications in Theory of Linear Operators

Fixed Point Theory and Applications volume 2007, Article number: 080987 (2007) Cite this article

Abstract

Some properties of the linear continuous operator and separation of convex subsets are investigated in this paper and a dual space for a subspace of a reflexive Banach space with a strictly convex norm is constructed. Here also an existence theorem and fixed-point theorem for general mappings are obtained. Moreover, certain remarks on the problem of existence of invariant subspaces of a linear continuous operator are given.

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  1. Department of Mathematics, Faculty of Sciences, Hacettepe University, Beytepe, Ankara, 06532, Turkey

    Kamal N Soltanov

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  1. Kamal N Soltanov
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Correspondence to Kamal N Soltanov.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Soltanov, K. Remarks on Separation of Convex Sets, Fixed-Point Theorem, and Applications in Theory of Linear Operators. Fixed Point Theory Appl 2007, 080987 (2007). https://doi.org/10.1155/2007/80987

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