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On Characterizations of Metric Regularity of Multi-valued Maps

Milen Ivanov, Nadia Zlateva

Abstract

We provide a new proof along the lines of the recent book of A. Ioffe of a 1990's result of H. Frankowska showing that metric regularity of a multi-valued map can be characterized by regularity of its contingent variation - a notion extending contingent derivative.

On Characterizations of Metric Regularity of Multi-valued Maps

Abstract

We provide a new proof along the lines of the recent book of A. Ioffe of a 1990's result of H. Frankowska showing that metric regularity of a multi-valued map can be characterized by regularity of its contingent variation - a notion extending contingent derivative.

Paper Structure

This paper contains 3 sections, 5 theorems, 41 equations.

Table of Contents

  1. Introduction
  2. Milyutin regularity
  3. Proof of the main result

Key Result

Theorem 1

Let $(X,d)$ be a metric space and $(Y,\| \cdot \|)$ be a Banach space, let $U\subset X$ and $V\subset Y$ be non-empty open sets. Let be a multi-valued map with complete graph. $F$ is restrictedly Milytin regular on $(U,V)$ with $\mathrm{sur} _m F^V(U\vert V)\ge r>0$ if and only if

Theorems & Definitions (13)

  • Theorem 1
  • Definition 2
  • Definition 3
  • Theorem 4
  • Definition 5
  • Definition 6
  • Theorem 7
  • proof
  • Definition 8
  • Lemma 9
  • ...and 3 more