A relaxed hybrid steepest descent method for common solutions of generalized mixed equilibrium problems and fixed point problems

作者：Onjai uea Nawitcha; Jaiboon Chaichana^*; Kumam Poom

来源：Fixed Point Theory and Applications, 2011, 32.

DOI：10.1186/1687-1812-2011-32

• relaxed hybrid steepest descent method
• inverse strongly monotone mappings
• nonexpansive mappings
• generalized mixed equilibrium problem

In the setting of Hilbert spaces, we introduce a relaxed hybrid steepest descent method for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of a variational inequality for an inverse strongly monotone mapping and the set of solutions of generalized mixed equilibrium problems. We prove the strong convergence of the method to the unique solution of a suitable variational inequality. The results obtained in this article improve and extend the corresponding results.

• 出版日期2011