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Some equivalent geometrical results with Ekeland’s variational principle. (English) Zbl 1134.46305

In this paper the author makes some interesting remarks on \(3\) well-known theorems in non-linear functional analysis. They are the Ekeland variational principle (EVP), the Drop theorem and the Flower petal theorem.
In Section \(2\) of the paper, the author considers modifications on the Ekeland’s variational principle and the Drop theorem.
It is shown in Section \(3\) that the modified form of EVP implies the generalized Drop theorem as well as the Flower petal theorem. The Flower petal theorem implies the generalized Drop theorem which in turn implies the EVP.

MSC:

46B20 Geometry and structure of normed linear spaces
46B99 Normed linear spaces and Banach spaces; Banach lattices
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