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

Kriengsak Wattanawitoon | Zendy; Poom Kumam | Zendy

Open Access

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

Author(s) -

Kriengsak Wattanawitoon,

Poom Kumam

Publication year - 2011

Publication title -

international journal of mathematics and mathematical sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.21

H-Index - 39

eISSN - 1687-0425

pISSN - 0161-1712

DOI - 10.1155/2011/174796

Subject(s) - mathematics , variational inequality , monotone polygon , strongly monotone , banach space , pseudo monotone operator , complementarity (molecular biology) , pure mathematics , convergence (economics) , discrete mathematics , mathematical analysis , finite rank operator , operator space , geometry , biology , economics , genetics , economic growth

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

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