A Hybrid Iterative Scheme for Mixed Equilibrium Problems, General System of Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces | Zendy

S. Imnang | Zendy; Suthep Suantai | Zendy

Open Access

A Hybrid Iterative Scheme for Mixed Equilibrium Problems, General System of Variational Inequality Problems, and Fixed Point Problems in Hilbert Spaces

Author(s) -

S. Imnang,

Suthep Suantai

Publication year - 2011

Publication title -

isrn mathematical analysis

Language(s) - English

Resource type - Journals

eISSN - 2090-4665

pISSN - 2090-4657

DOI - 10.5402/2011/837809

Subject(s) - variational inequality , hilbert space , fixed point , mathematics , sequence (biology) , scheme (mathematics) , iterative method , set (abstract data type) , element (criminal law) , mathematical optimization , mathematical analysis , computer science , genetics , political science , law , biology , programming language

We introduce a new iterative scheme for finding a common element of the set of solutions of a general system of variational inequalities, the set of solutions of a mixed equilibrium problem, and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Using the demiclosedness principle for nonexpansive mappings, we prove that the iterative sequence converges strongly to a common element of the above three sets under some control conditions, and we also give some examples for mappings which satisfy conditions of the main result.

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