Two extragradient methods for generalized mixed equilibrium problems, nonexpansive mappings and monotone mappings

✍ Scribed by Jian-Wen Peng; Jen-Chih Yao

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 889 KB
• Volume: 58
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2009.07.040

✦ Synopsis

In this paper, we introduce iterative schemes based on the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of an infinite (a finite) family of nonexpansive mappings and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. We obtain some weak convergence theorems for the sequences generated by these processes in Hilbert spaces. The results in this paper generalize, extend and unify some well-known weak convergence theorems in the literature.