Remarks on separation of convex sets, fixed-point theorem, and applications in theory of linear operators

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Soltanov K. N.

FIXED POINT THEORY AND APPLICATIONS, 2007 (SCI-Expanded)

• Publication Type: Article / Article
• Volume:
• Publication Date: 2007
• Doi Number: 10.1155/2007/80987
• Journal Name: FIXED POINT THEORY AND APPLICATIONS
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Hacettepe University Affiliated: No

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.