Set-Valued Analysis

, Volume 6, Issue 2, pp 171–185

The Equivalence of Several Basic Theorems for Subdifferentials

  • Qiji J. Zhu
Article

DOI: 10.1023/A:1008656207314

Cite this article as:
Zhu, Q.J. Set-Valued Analysis (1998) 6: 171. doi:10.1023/A:1008656207314

Abstract

Several different basic tools are used for studying subdifferentials. They are a nonlocal fuzzy sum rule in (Borwein et al., 1996; Zhu, 1996), a multidirectional mean value theorem in (Clarke and Ledyaev, 1994; Clarke et al., 1998), local fuzzy sum rules in (Ioffe, 1984, 1990) and an extremal principle in (Kruger and Mordukhovich, 1980; Mordukhovich, 1976, 1980, 1994). We show that all these basic results are equivalent and discuss some interesting consequences of this equivalence.

subdifferentialsmean value inequalitieslocal fuzzy sum rulesnonlocal fuzzy sum rulesextremal principles and Asplund spaces

Copyright information

© Kluwer Academic Publishers 1998

Authors and Affiliations

  • Qiji J. Zhu
    • 1
  1. 1.Department of Mathematics and StatisticsWestern Michigan UniversityKalamazooU.S.A.