On Gâteaux differentiability of strongly cone paraconvex vector-valued mappings. (3rd October 2019) - Bednarczuk, E. M.; Leśniewski, K. W.
ABSTRACT: We prove that a strongly cone paraconvex mapping defined on a normed space X and taking values in a reflexive separable Banach space Y is Gâteaux differentiable on a dense G δ subset of X . We also discuss Fréchet differentiability in the case when X is an Asplund space. Our results are generalizations of Rolewicz's theorems (Theorem 3.1) from Rolewicz [Differentiability of strongly paraconvex vector-valued functions. Funct Approx. 2011;2:273–277].