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

作者：Sunthrayuth Pongsakorn; Kumam Poom^*

来源：Fixed Point Theory and Applications, 2012, 2012(1): 1-17.

DOI：10.1186/1687-1812-2012-65

• strict pseudo-contractions
• variational inequality
• strong convergence theorem
• q-uniformly smooth Banach space
• common fixed point

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.

• 出版日期2012