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Displaying similar documents to “Sharp norm estimate of Schwarzian derivative for a class of convex functions”

Remarks on strongly Wright-convex functions

Nelson Merentes, Kazimierz Nikodem, Sergio Rivas (2011)

Annales Polonici Mathematici

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Some properties of strongly Wright-convex functions are presented. In particular it is shown that a function f:D → ℝ, where D is an open convex subset of an inner product space X, is strongly Wright-convex with modulus c if and only if it can be represented in the form f(x) = g(x)+a(x)+c||x||², x ∈ D, where g:D → ℝ is a convex function and a:X → ℝ is an additive function. A characterization of inner product spaces by strongly Wright-convex functions is also given.