An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α (·)-paraconvex functions
S. Rolewicz (2006)
Studia Mathematica
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Let (X,||·||) be a separable real Banach space. Let f be a real-valued strongly α(·)-paraconvex function defined on an open convex subset Ω ⊂ X, i.e. such that . Then there is a dense -set such that f is Gateaux differentiable at every point of .