, Volume 132, Issue 3, pp 493-507
Date: 16 May 2007

Generalization of Ordering Principles and Applications

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Abstract

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.

Communicated by X.Q. Yang.
This work was completed while the first author was visiting the Institute of Mathematics and Systems Sciences of the Chinese Academy of Sciences and was supported by NNSF (10671167), EDJPNSF (05KGD110225) and JSQLGCF (QL200502) China. The authors are grateful to the Associate Editor and the referees for careful reading of the paper and significant suggestions.