Set-Valued Analysis

, Volume 6, Issue 2, pp 171–185

The Equivalence of Several Basic Theorems for Subdifferentials

  • Qiji J. Zhu

DOI: 10.1023/A:1008656207314

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


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.

subdifferentials mean value inequalities local fuzzy sum rules nonlocal fuzzy sum rules extremal 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.

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