Journal of Convex Analysis 15 (2008), No. 2, 395--409
Copyright Heldermann Verlag 2008
Maximal Monotone Operators and Maximal Monotone Functions for Equilibrium Problems
Koji Aoyama
Dept. of Economics, Chiba University, Yayoi-cho, Inage-ku, Chiba-shi, Chiba 263-8522, Japan
aoyama@le.chiba-u.ac.jp
Yasunori Kimura
Dept. of Mathematical and Computing Sciences, Tokyo Inst. of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan
yasunori@is.titech.ac.jp
Wataru Takahashi
Dept. of Mathematical and Computing Sciences, Tokyo Inst. of Technology, Ookayama, Meguro-ku, Tokyo 152-8552, Japan
wataru@is.titech.ac.jp
We deal with multivalued monotone operators and two variable monotone functions for equilibrium problems in Banach spaces. We first study close relationships concerning resolvents and maximal monotonicity for monotone operators and monotone functions. We also consider a one-to-one correspondence between a class of maximal monotone operators and that of maximal monotone functions with certain conditions.
Keywords: Equilibrium problem, maximal monotone operator, maximal monotone function, resolvent.
MSC: 47H05, 74G10
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