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A Brézis-Browder principle on partially ordered spaces and related ordering theorems |
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| Authors: | F. Flores-Bazá n,V. Novo |
| Affiliation: | a Departamento de Ingeniería Matemática, Facultad de Ciencias Físicas y Matemáticas, Universidad de Concepción, Casilla 160-C, Concepción, Chile b Departamento de Matemática Aplicada, E.T.S.I. Informática, Universidad de Valladolid, Edificio de Tecnologías de la Información y las Telecomunicaciones, Paseo de Belén, 15, Campus Miguel Delibes, s/n, 47011 Valladolid, Spain c Departamento de Matemática Aplicada, E.T.S.I. Industriales, Universidad Nacional de Educación a Distancia, c/ Juan del Rosal, 12, Ciudad Universitaria, 28040 Madrid, Spain |
| Abstract: | Through a simple extension of Brézis-Browder principle to partially ordered spaces, a very general strong minimal point existence theorem on quasi ordered spaces, is proved. This theorem together with a generic quasi order and a new notion of strong approximate solution allow us to obtain two strong solution existence theorems, and three general Ekeland variational principles in optimization problems where the objective space is quasi ordered. Then, they are applied to prove strong minimal point existence results, generalizations of Bishop-Phelps lemma in linear spaces, and Ekeland variational principles in set-valued optimization problems through a set solution criterion. |
| Keywords: | Quasi order Existence of strong minimal points Ordering principle Bré zis-Browder principle Bishop-Phelps lemma Ekeland variational principle Vector optimization Set-valued optimization Set solution criterion Existence of strong efficient solutions |
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