Near Convexity and Generalized Differentiation

TL;DR

This paper introduces nearly convex set-valued mappings, explores their fundamental properties, and develops a geometric approach for their generalized differentiation, expanding the theoretical framework of nearly convex analysis.

Contribution

It presents new results on nearly convex set-valued mappings and a geometric method for their generalized differentiation, advancing the understanding of nearly convex analysis.

Findings

Introduction of nearly convex set-valued mappings

Development of a geometric approach for generalized differentiation

New theoretical results on nearly convex functions and sets

Abstract

In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex set-valued mappings and nearly convex functions. Our contributions expand the current knowledge of nearly convex sets and functions, while providing several new results pertaining to nearly convex set-valued mappings.