Maximal Monotone Operators and Maximal Monotone Functions for Equilibrium Problems

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.