Journal of Inequalities and Applications
Volume 2007 (2007), Article ID 46041, 25 pages
Equivalent Solutions of Nonlinear Equations in a Topological Vector Space with a Wedge
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.