Abstract
In this paper, we first introduce a new hybrid iteration method for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces, and then we discuss the strong and weak convergence for the iterative processes. The results presented in this paper extend and improve the corresponding results of Wang and Osilike.
Highlights
1 Introduction and preliminaries Throughout this paper we assume that E is a real Banach space and T : E → E is a mapping
The convergence problems of an implicit iterative process to a common fixed point for a finite family of asymptotically nonexpansive mappings in Hilbert spaces or uniformly convex Banach spaces have been considered by several authors
We introduce the following new hybrid iteration method in Banach spaces: m xn+ = αnxn + ( – αn) τiTinxn – λn+ μf i=
Summary
Introduction and preliminariesThroughout this paper we assume that E is a real Banach space and T : E → E is a mapping. ( ) T is said to be asymptotically nonexpansive [ ] if there exists a sequence {kn} ⊂ [ , ∞) with limn→∞ kn = such that M, Ti : K → K is an asymptotically nonexpansive mapping, there exists a sequence {kn(i)} ⊂ [ , ∞) with kn(i) → (n → ∞) such that
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