Maximal Monotone Operators and Maximal Monotone Functions for Equilibrium Problems

Koji Aoyama; Yasunori Kimura; Wataru Takahashi

Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

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

Keywords

Equilibrium problem
maximal monotone operator
maximal monotone function
resolvent

Mathematics Subject Classification

47H05, 74G10

Suggested citation

K. Aoyama, Y. Kimura, W. Takahashi. “Maximal Monotone Operators and Maximal Monotone Functions for Equilibrium Problems.” Journal of Convex Analysis 15 (2008), No. 2, 395–409.