Journal of Convex Analysis 19 (2012), No. 3, 713--724
Copyright Heldermann Verlag 2012
Approaching the Maximal Monotonicity of Bifunctions via Representative Functions
Radu Ioan Bot
Dept. of Mathematics, University of Technology, 09107 Chemnitz, Germany
bot@mathematik.tu-chemnitz.de
Sorin-Mihai Grad
Dept. of Mathematics, University of Technology, 09107 Chemnitz, Germany
grad@mathematik.tu-chemnitz.de
We provide an approach to maximal monotone bifunctions based on the theory of representative functions. Thus we extend to nonreflexive Banach spaces recent results due to A. N. Iusem ["On the maximal monotonicity of diagonal subdifferential operators", J. Convex Analysis 18 (2011) 489--503] and, respectively, to N. Hadjisavvas and H. Khatibzadeh ["Maximal monotonicity of bifunctions", Optimization 59 (2010) 147--160], where sufficient conditions guaranteeing the maximal monotonicity of bifunctions were introduced. New results involving the sum of two monotone bifunctions are also presented.
Keywords: Conjugate functions, subdifferentials, representative functions, maximal monotone bifunctions, maximal monotone operators.
MSC: 47H05; 42A50, 90C25
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