A Minimal Point Theorem in Uniform Spaces
SubjectMinimal point theorem; Set-valued variational principle; Fixed point theorem; Uniform spaces
We present a minimal point theorem in a product space X × Y , X being a separated uniform space, Y a topological vector space under the weakest assumptions up to now. We state Ekeland’s variational prin- ciple and Kirk–Caristi’s fixed point theorem for set–valued maps and show the equivalence of all the three theorems. Using a new characterization of uniform spaces we show that our theorems generalize several recent results.
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Hamel AH; Löhne A (YOKOHAMA PUBL, 2006)We present two existence principles for minimal points of subsets of the product space X × 2Y, where X stands for a separated uniform space and Y a topological vector space. The two principles are distinct with respect to ...
Hamel AH (Elsevier, 2005)A minimal element theorem on sequentially complete uniform spaces is presented that generalizes earlier results of [Pacific J. Math. 55(2) (1974) 335–341; Proc. Amer. Math. Soc. 108(3) (1990) 707–714]. Two more equivalent ...
Hamel AH (2003)A generalization of Phelps' lemma to locally convex spaces is proven, applying its well-known Banach space version. We show the equivalence of this theorem, Ekeland's principle and Danes' drop theorem in locally convex ...