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.
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Zagrodny, D. The maximal monotonicity of the subdifferentials of convex functions: Simons' problem. Set-Valued Anal 4, 301–314 (1996). https://doi.org/10.1007/BF00436107
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DOI: https://doi.org/10.1007/BF00436107