A relaxed hybrid steepest descent method for common solutions of generalized mixed equilibrium problems and fixed point problems
Nawitcha Onjai-uea, Chaichana Jaiboon, Poom Kumam · Fixed Point Theory and Applications · 2011
Abstract 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. AMS (2000) Subject Classification: 46C05; 47H09; 47H10.