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Generalization of ordering principles and applications. (English) Zbl 1146.49016
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:
49J53Set-valued and variational analysis
47H04Set-valued operators
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47N10Applications of operator theory in optimization, convex analysis, programming, economics
54H25Fixed-point and coincidence theorems in topological spaces
References:
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