On the weak convergence of iterative sequences for generalized equilibrium problems and strictly pseudocontractive mappings

Abstract

In this article we consider the problem of finding a common element in the solution set of generalized equilibrium problems, in the solution set of the classical variational inequality and in the fixed point set of strictly pseudocontractive mappings. Weak convergence theorems of common elements are established in real Hilbert spaces.

Keywords:

• equilibrium problem
• variational inequality
• strictly pseudocontractive mapping
• nonexpansive mapping
• inverse-strongly monotone mapping

AMS Subject Classifications:

• 47H05
• 47H09
• 47J25

Acknowledgements

This work was supported by the Kyungnam University research Fund 2009.