Weak and strong convergence theorems of implicit iteration process on Banach spaces

作者：Lin, Lai-Jiu^*; Chuang, Chih-Sheng; Yu, Zenn-Tsun

来源：Fixed Point Theory and Applications, 2011, 2011(1): 96.

DOI：10.1186/1687-1812-2011-96

• FIXED-POINT THEOREMS
• NONEXPANSIVE-MAPPINGS
• FAMILIES

In this article, we first consider weak convergence theorems of implicit iterative processes for two nonexpansive mappings and a mapping which satisfies condition (C). Next, we consider strong convergence theorem of an implicit-shrinking iterative process for two nonexpansive mappings and a relative nonexpansive mapping on Banach spaces. Note that the conditions of strong convergence theorem are different from the strong convergence theorems for the implicit iterative processes in the literatures. Finally, we discuss a strong convergence theorem concerning two nonexpansive mappings and the resolvent of a maximal monotone operator in a Banach space.

• 出版日期2011
• 单位南开大学