Some convergence theorems of the Mann iteration for monotone α-nonexpansive mappings
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Author list: Song Y., Promluang K., Kumam P., Je Cho Y.
Publisher: Elsevier
Publication year: 2016
Journal: Applied Mathematics and Computation (0096-3003)
Volume number: 287-288
Start page: 74
End page: 82
Number of pages: 9
ISSN: 0096-3003
eISSN: 1873-5649
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we introduce the concept of monotone α-nonexpansive mappings in an ordered Banach space E with the partial order ≤, which contains monotone nonexpansive mappings as special case. With the help of the Mann iteration, we show some existence theorems of fixed points of monotone α-nonexpansive mappings in uniformly convex ordered Banach space. Also, we prove some weak and strong convergence theorems of the Mann iteration for finding an order fixed point of monotone α-nonexpansive mappings under the condition lim supn→∞βn(1-βn)>0orlim infn→∞βn(1-βn)>0. © 2016 Elsevier Inc. All rights reserved.
Keywords
Monotone α-nonexpansive mapping
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