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  • Research Article
  • Open Access

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

Journal of Inequalities and Applications20072007:046041

https://doi.org/10.1155/2007/46041

  • Received: 31 December 2006
  • Accepted: 28 May 2007
  • Published:

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.

Keywords

  • Vector Space
  • Nonlinear Equation
  • Continuity Condition
  • Topological Vector Space
  • Efficient Condition

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Authors’ Affiliations

(1)
Institute of Mathematics, Academy of Sciences of the Czech Republic, Žižkova 22, Brno, 61662, Czech Republic

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