On the Directonal Derivative Sets and Differentials of the Set Valued Maps

TL;DR

This paper investigates the properties of directional derivative sets and differentials of set-valued maps, exploring their relations with compact subsets and calculating contingent cones for certain plane sets.

Contribution

It introduces new relations between set-valued maps and their directional derivative sets, and computes contingent cones for specific plane sets.

Findings

Relations between set-valued maps and compact subsets of derivative sets

Calculations of upper and lower contingent cones for plane sets

Insights into the structure of directional derivatives of set-valued maps

Abstract

In this paper directional derivative sets and differentials of a given set valued map are studied. Relations between the set valued map and compact subsets of the directional derivative sets of the given map are investigated. Upper and lower contingent cones of some plane sets are calculated.