Stability of iterative procedures with errors for approximating common fixed points of quasi-contractive mappings

Abstract

In this article, we introduce a new class of iterative sequences with errors for approximating the common fixed point of a couple of quasi-contractive mappings and show the stability of the iterative procedures with errors in q-uniformly smooth Banach spaces. Our results extend, improve and unify the corresponding results of Agarwal, Cho, Li, Huang, Chidume, Osilike, Liu, and others.

Keywords:

• Stability
• Iterative procedures with errors
• A couple of quasi-contractive mappings
• Common fixed point
• q-uniformly smooth Banach space
• AMS (MOS) Subject Classifications: 47H10
• 40A05

Acknowledgement

The work was supported by the National Natural Science Foundation of China, the China West Normal University Scientific Research Fund (2000-3), and the Korea Research Foundation Grant (KRF-2003-002-C00018).