Weak and strong convergence theorems for a countable family of strict pseudocontractions in Banach spaces

Abstract

We first investigate the weak convergence of the Mann-type iterative scheme for a countable family of strict pseudocontractions in a uniformly smooth Banach space which is uniformly convex or satisfies Opial's condition. Then the strong convergence theorems of the modified Mann-type iterative scheme are also proved in a uniformly smooth Banach space. As a consequence, several weak and strong convergence theorems for an infinite family of pseudocontractions are established.

Keywords:

• common fixed points
• convergence theorem
• Mann iteration
• strict pseudocontractions
• uniformly smooth Banach spaces

AMS Subject Classifications::

• 47H09
• 47H10

Acknowledgements

The authors thank the referees for valuable suggestions on improvement of this manuscript and we wish to thank the National Research University Project under Thailand's Office of the Higher Education Commission for financial support. Prasit Cholamjiak was supported by the Royal Golden Jubilee Grant PHD/0261/2551 and by the Graduate School, Chiang Mai University, Thailand.