Set-Valued Analysis

, Volume 4, Issue 4, pp 301–314 | Cite as

The maximal monotonicity of the subdifferentials of convex functions: Simons' problem

  • Dariusz Zagrodny
Article
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Abstract

In the paper we deal with the problem when the graph of the subdifferential operator of a convex lower semicontinuous function has a common point with the product of two convex nonempty weak and weak* compact sets, i.e. when graph ∂ψ ∩ (Q × Q*) ≠ 0. The results obtained partially solve the problem posed by Simons as well as generalize the Rockafellar Maximal Monotonicity Theorem.

Mathematics Subject Classifications (1991)

49J52 26B25 47H05 52A10 52A41 

Key words

convex functions subdifferentials maximal monotonicity graph of subdifferential convex sets orthogonality 
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Copyright information

© Kluwer Academic Publishers 1996

Authors and Affiliations

  • Dariusz Zagrodny
    • 1
  1. 1.Technical University of ŁódźŁódźPoland

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