A Remark on the Lower Semicontinuity Assumption in the Ekeland Variational Principle
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چکیده
What happens to the conclusion of the Ekeland variational principle (briefly, EVP) if a considered function f : X → R ∪ {+∞} is lower semicontinuous not on a whole metric space X but only on its domain? We provide a straightforward proof showing that it still holds but only for varying in some interval ]0, β − infX f [, where β is a quantity expressing quantitatively the violation of the lower semicontinuity of f outside its domain. The obtained result extends EVP to a larger class of functions.
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