Iterative methods for variational inequality problems and fixed point problems of a countable family of strict pseudo-contractions in a q -uniformly smooth Banach space

Fixexd point theory and applications

Pongsakorn Sunthrayuth²  Poom Kumam³ 

[1] Centre of Excellence in Mathematics, CHE, Bangkok, Thailand;Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi (KMUTT) Bangmod, Bangkok, Thailand

关键词: strict pseudo-contractions;    variational inequality;    strong convergence theorem;    q-uniformly smooth Banach space;    common fixed point;   

DOI  :  10.1186/1687-1812-2012-65

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this article, we introduce iterative methods (implicit and explicit) for finding a common fixed point set of a countable family of strict pseudo-contractions, which is a unique solution of some variational inequality. Furthermore, we prove the strong convergence theorems of such iterative scheme in a q-uniformly smooth Banach space which admits a weakly sequentially continuous generalized duality mapping. The results presented in this article extend and generalize the corresponding results announced by Yamada and Ceng et al. from Hilbert spaces to Banach spaces. Mathematics Subject Classification 2010: 47H09; 47J05; 47J20; 65J15.

【 授权许可】

CC BY