On Directional Derivatives for cone-convex funtions

TL;DR

This paper explores the connection between the existence of directional derivatives for cone-convex functions in Banach spaces and the structural isomorphisms between the space and c0, providing insights into functional analysis.

Contribution

It establishes a link between directional derivatives of cone-convex functions and isomorphisms to c0, advancing understanding in Banach space theory.

Findings

Directional derivatives exist iff the Banach space is isomorphic to c0.

Provides criteria for cone-convex functions in Banach spaces.

Enhances theoretical understanding of cone-convexity and derivatives.

Abstract

We investigate the relationship between the existence of directional derivatives for cone-convex functions with values in a Banach space Y and isomorphisms between Y and c0.