On G\^ateaux differentiability of strongly cone paraconvex vector-valued mappings

TL;DR

This paper studies the conditions under which strongly cone paraconvex vector-valued mappings are Gâteaux and Fréchet differentiable, advancing the understanding of their smoothness properties.

Contribution

It provides new insights into the differentiability of strongly cone paraconvex vector-valued mappings, focusing on Gâteaux and Fréchet differentiability criteria.

Findings

Established conditions for Gâteaux differentiability.

Analyzed Fréchet differentiability in the context of cone paraconvexity.

Extended differentiability results to variable order paraconvex mappings.

Abstract

We investigate the G\^ateaux and Fr\^echet differentiabilities of strongly ${\alpha(\cdot)}$-$k$-paraconvex vector-valued mappings.