On the existence of directional derivatives for strongly cone-paraconvex mappings

TL;DR

This paper investigates the conditions under which strongly cone-paraconvex mappings possess directional derivatives, extending Valadier's theorem on cone convex mappings to a broader class of functions.

Contribution

It provides a new theoretical result establishing the existence of directional derivatives for strongly cone-paraconvex mappings, expanding the understanding of their differentiability properties.

Findings

Established the existence of directional derivatives for strongly cone-paraconvex mappings.

Extended Valadier's theorem to a broader class of mappings.

Contributed to the theory of cone-paraconvex functions and their differentiability.

Abstract

In the present paper we investigate the existence of directional derivatives for strongly cone-paraconvex mappings. Our result is a counterpart of the theorem of Valadier concerning directional differentiability of cone convex mappings.