Hybrid Proximal-Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems

摘要

We prove strong and weak convergence theorems of modified hybrid proximal-pointalgorithms for finding a common element of the zero point of a maximal monotone operator, the setof solutions of equilibrium problems, and the set of solution of the variational inequality operators ofan inverse strongly monotone in a Banach space under different conditions. Moreover, applications tocomplementarity problems are given. Our results modify and improve the recently announced ones byLi and Song (2008) and many authors.