Some convergence theorems of the Mann iteration for monotone α-nonexpansive mappings

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• 作者：Yisheng Song^a ; ^{songyisheng@htu.cn" class="auth_mail" title="E-mail the corresponding author} ; Khanittha Promluang^b ; ^{k.promluang@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Poom Kumam ; ¹ ; ^c ; ^d ; ^{poom.kum@kmutt.ac.th" class="auth_mail" title="E-mail the corresponding author} ; ^{poom.kumam@mail.kmutt.ac.th" class="auth_mail" title="E-mail the corresponding author} ; ^{poom.kum@mail.cmu.edu.tw" class="auth_mail" title="E-mail the corresponding author} ; Yeol Je Cho ; ² ; ^e ; ^f ; ^{yjcho@gnu.ac.kr" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Ordered Banach space ; Fixed point ; Monotone α-nonexpansive mapping ; Convergence ; The Mann iteration
• 刊名：Applied Mathematics and Computation
• 出版年：2016
• 出版时间：5 September 2016
• 年：2016
• 卷：287-288
• 期：Complete
• 页码：74-82
• 全文大小：343 K

文摘

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