Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 46041, 25 pages
Research Article

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

A. Rontó and J. Šremr

Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, Brno 61662, Czech Republic

Received 31 December 2006; Revised 20 May 2007; Accepted 28 May 2007

Academic Editor: Simeon Reich

Copyright © 2007 A. Rontó and J. Šremr. 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.


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.