Journal of Inequalities and Applications 
Volume 2007 (2007), Article ID 46041, 25 pages
doi:10.1155/2007/46041
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

Recommended by Simeon Reich

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.