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  • Research Article
  • Open Access

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

Fixed Point Theory and Applications20072007:080987

https://doi.org/10.1155/2007/80987

  • Received: 20 February 2007
  • Accepted: 2 May 2007
  • Published:

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.

Keywords

  • Banach Space
  • General Mapping
  • Linear Operator
  • Differential Geometry
  • Convex Subset

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Authors’ Affiliations

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

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