On Gâteaux differentiability of strongly cone paraconvex vector-valued mappings. (3rd October 2019)

• Record Type: Journal Article
• Authors: Bednarczuk, E. M.; Leśniewski, K. W.
• Is Part Of: Optimization. Volume 68:Number 10(2019)
• Page Start: 2025
• Page End: 2037
• Publication Date: 2019-10-03
• Subjects: Directional derivative -- Fréchet differentiability -- strongly paraconvex mappings -- cone convex mappings -- vector-valued mappings -- separable Banach spaces; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2019.1653296
• Languages: English
• ISSNs: 0233-1934

Abstract

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].