Hybrid Algorithms for Minimization Problems over the Solutions of Generalized Mixed Equilibrium and Variational Inclusion Problems | Zendy

Thanyarat Jitpeera | Zendy; Poom Kumam | Zendy

Open Access

Hybrid Algorithms for Minimization Problems over the Solutions of Generalized Mixed Equilibrium and Variational Inclusion Problems

Author(s) -

Thanyarat Jitpeera,

Poom Kumam

Publication year - 2011

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2011/648617

Subject(s) - hilbert space , sequence (biology) , mathematics , monotone polygon , set (abstract data type) , element (criminal law) , algorithm , inverse , variational inequality , solution set , strongly monotone , convergence (economics) , minification , space (punctuation) , fixed point , mathematical optimization , mathematical analysis , computer science , geometry , genetics , political science , law , economics , biology , programming language , economic growth , operating system

We introduce a new general hybrid iterative algorithm for finding a commonelement of the set of solution of fixed point for a nonexpansive mapping, the set of solution ofgeneralized mixed equilibrium problem, and the set of solution of the variational inclusion for a β-inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence convergesstrongly to a common element of the above three sets under some mild conditions. Our results improveand extend the corresponding results of Marino and Xu (2006), Yao and Liou (2010), Tan and Chang(2011), and other authors

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