The Convexity of the Closure of the Domain and the Range of a Maximal Monotone Multifunction of Type NI

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• 作者：Dariusz Zagrodny
• 关键词：Nonlinear operators ; Monotone operator ; Multifunctions of type NI ; Domain of maximal monotone operator ; Range of maximal monotone operator ; The Fitzpatrick function ; Subdiferential of the Fitzpatrick function ; Perfect square criterion for the maxim
• 刊名：Set-Valued Analysis
• 出版年：2008
• 出版时间：December, 2008
• 年：2008
• 卷：16
• 期：5-6
• 页码：759-783
• 全文大小：489.9 KB

文摘

It is shown that the closure of the domain and the closure of the range of a maximal monotone set of type NI are convex sets. This is a positive answer to the question concerning the convexity of the closure of the range of a maximal monotone multifunction, posed in Simons (Minimax and Monotonicity, Lecture Notes in Mathematics 1693. Springer-Verlag, Berlin, 1998, X Open Problems, Problem 27.7).