Iterative methods for mixed equilibrium problems and strictly pseudocontractive mappings

作者：Jung Jong Soo^*

来源：Fixed Point Theory and Applications, 2012, 184.

DOI：10.1186/1687-1812-2012-184

• mixed equilibrium problem
• k-strictly pseudocontractive mapping
• nonexpansive mapping
• fixed points
• rho-Lipschitzian and eta-strongly monotone operator
• variational inequality

In this paper, we introduce new implicit and explicit iterative schemes for finding a common element of the set of solutions of the mixed equilibrium problem and the set of fixed points of a k-strictly pseudocontractive non-self mapping in Hilbert spaces. We establish results of the strong convergence of the sequences generated by the proposed schemes to a common point of two sets, which is a solution of a certain variational inequality. Our results extend and improve the corresponding results given by many authors recently in this area.

• 出版日期2012