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

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

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We prove strong and weak convergence theorems of modified hybrid proximal-point algorithms for here 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 harry potter magsafe case recently announced ones by Li and Song (2008) and many authors.