
Journal of Convex Analysis 15 (2008), No. 2, 395409 Copyright Heldermann Verlag 2008 Maximal Monotone Operators and Maximal Monotone Functions for Equilibrium Problems Koji Aoyama Dept. of Economics, Chiba University, Yayoicho, Inageku, Chibashi, Chiba 2638522, Japan aoyama@le.chibau.ac.jp Yasunori Kimura Dept. of Mathematical and Computing Sciences, Tokyo Inst. of Technology, Ookayama, Meguroku, Tokyo 1528552, Japan yasunori@is.titech.ac.jp Wataru Takahashi Dept. of Mathematical and Computing Sciences, Tokyo Inst. of Technology, Ookayama, Meguroku, Tokyo 1528552, 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 onetoone 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 [ Fulltextpdf (140 KB)] for subscribers only. 