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Zbl 1146.49016
Zhu, J.; Li, S.J.
Generalization of ordering principles and applications. (English)
[J] J. Optim. Theory Appl. 132, No. 3, 493-507 (2007). ISSN 0022-3239; ISSN 1573-2878/e

Summary: In this paper, we prove some new ordering principles which generalize the well-known Brézis-Browder principle and uniformly generalize some results in the literature. As an application, we prove some vector Ekeland-type variational principles in F-type topological spaces and some new Mönch-type fixed-point theorems for discontinuous multivalued operators in F-type topological spaces and Banach spaces with weak topology.

MSC 2000:: *49J53 Set-valued and variational analysis
47H04 Set-valued operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47N10 Appl. of operator theory in optimization, math. programming, etc.
54H25 Fixed-point theorems in topological spaces

Keywords: maximal elements; Ekeland variational principle; fixed points; multivalued operators

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Zentralblatt MATH Berlin [Germany]