New relaxed hybrid-extragradient method for fixed point problems, a general system of variational inequality problems and generalized mixed equilibrium problems

Abstract

In this article, we present a new iterative method based on the relaxed hybrid method and the extragradient method for finding a common element of the set of solutions of generalized equilibrium problems and the set of fixed points of a strictly pseudocontractive mapping and the set of a general system of variational inequality with inverse strongly monotone mappings in a real Hilbert space. Furthermore, we prove that the proposed iterative method has strong convergence under some mild conditions imposed on algorithm parameters.

Keywords:

• mixed equilibrium problem
• fixed point
• monotone mapping
• pseudocontractive mapping
• general system of variational inequalities

AMS Subject Classifications::

• 47H05
• 47H10
• 49J30
• 49J40

Acknowledgements

Yeong-Cheng Liou was partially supported by the grant NSC 97-2221-E-230-017 and Jen-Chih Yao was partially supported by the grant HSC-96-2628-E-110-014-MY3.