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

Yisheng Song, Khanittha Promluang, Poom Kumam and Yeol Je Cho

Applied Mathematics and Computation, 2016, vol. 287-288, 74-82

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.

Keywords: Ordered Banach space; Fixed point; Monotone α-nonexpansive mapping; Convergence; The Mann iteration (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:287-288:y:2016:i::p:74-82

DOI: 10.1016/j.amc.2016.04.011

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