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• W4286906266 abstract "It is well known that in the calculus of variations and in optimization there exist many formulations of the fundamental propositions on the attainment of the infima of sequentially weakly lower semicontinuous coercive functions on reflexive Banach spaces. By either some constructive skills or the regularization skill by inf–convolutions we show in this paper that all these formulations together with their important variants are equivalent to each other and equivalent to the reflexivity of the underlying space. Motivated by this research, we also give a characterization for a normed space to be finite dimensional: a normed space is finite dimensional iff every continuous real–valued function defined on each bounded closed subset of this space can attain its minimum, namely the converse of the classical Weierstrass theorem also holds true." @default.
• W4286906266 created "2022-07-25" @default.
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• W4286906266 date "2023-03-01" @default.
• W4286906266 modified "2023-10-16" @default.
• W4286906266 title "Some nonlinear characterizations of reflexive Banach spaces" @default.
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• W4286906266 doi "https://doi.org/10.1016/j.jmaa.2022.126736" @default.
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