Hybrid Proximal‐Point Methods for Zeros of Maximal Monotone Operators, Variational Inequalities and Mixed Equilibrium Problems
Kriengsak Wattanawitoon, Poom Kumam · International Journal of Mathematics and Mathematical Sciences · 2011
We prove strong and weak convergence theorems of modified hybrid proximal‐point algorithms for finding a common element of the zero point of a maximal monotone operator, the set of solutions of equilibrium problems, and the set of solution of the variational inequality operators of an inverse strongly monotone in a Banach space under different conditions. Moreover, applications to complementarity problems are given. Our results modify and improve the recently announced ones by Li and Song (2008) and many authors.