Open Access

Equivalent Solutions of Nonlinear Equations in a Topological Vector Space with a Wedge

Journal of Inequalities and Applications20072007:046041

DOI: 10.1155/2007/46041

Received: 31 December 2006

Accepted: 28 May 2007

Published: 5 July 2007

Abstract

We obtain efficient conditions under which some or all solutions of a nonlinear equation in a topological vector space preordered by a closed wedge are comparable with respect to the corresponding preordering. Conditions sufficient for the equivalence of comparable solutions are also given. The wedge under consideration is not assumed to be a cone, nor any continuity conditions are imposed on the mappings considered.

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Authors’ Affiliations

(1)
Institute of Mathematics, Academy of Sciences of the Czech Republic

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Copyright

© A. Rontó and J. ŠSremr. 2007

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.