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 skylight quilt pattern 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 medline remedy phytoplex protectant z-guard paste 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.