Suppose that K is a nonempty closed convex subset of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let T 1 , T 2 : K โ E be two asymptotically nonexpansive nonself-mappings with sequences where {ฮฑ n } and {ฮฒ n } are two real sequences in [ฯต, 1 -ฯต] for some ฯต > 0. If E
Convergence theorems for nonself asymptotically nonexpansive mappings
โ Scribed by Safeer Hussain Khan; Nawab Hussain
- Publisher
- Elsevier Science
- Year
- 2008
- Tongue
- English
- Weight
- 253 KB
- Volume
- 55
- Category
- Article
- ISSN
- 0898-1221
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โฆ Synopsis
In this paper, we prove some strong and weak convergence theorems using a modified iterative process for nonself asymptotically nonexpansive mappings in a uniformly convex Banach space. This will improve and generalize the corresponding results in the existing literature. Finally, we will state that our theorems can be generalized to the case of finitely many mappings.
๐ SIMILAR VOLUMES
In this paper, we study boundary conditions for nonexpansive nonself-mappings in a Banach space. Using this, we prove two strong convergence theorems for nonexpansive nonself-mappings in a Banach space without boundary conditions.