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

Fixed Point Theory and Applications20072007:080987

DOI: 10.1155/2007/80987

Received: 20 February 2007

Accepted: 2 May 2007

Published: 5 July 2007


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.


Authors’ Affiliations

Department of Mathematics, Faculty of Sciences, Hacettepe University


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© Kamal N. Soltanov. 2007

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