An extension of Mazur's theorem on Gateaux differentiability to the class of strongly α(⋅)-paraconvex functions
Stefan Rolewicz · Studia Mathematica · 2006
Let $(X,\| \cdot \| )$ be a separable real Banach space. Let $f$ be a real-valued strongly $\alpha (\cdot )$-paraconvex function defined on an open convex subset ${\mit \Omega } \subset X$, i.e. such that $$ f(tx+(1-t)y) \leq tf(x)+(1-t)f(y) + \mathop {\r