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

Author

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

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.

Suggested Citation

  • Song, Yisheng & Promluang, Khanittha & Kumam, Poom & Je Cho, Yeol, 2016. "Some convergence theorems of the Mann iteration for monotone α-nonexpansive mappings," Applied Mathematics and Computation, Elsevier, vol. 287, pages 74-82.
    • Handle: RePEc:eee:apmaco:v:287-288:y:2016:i::p:74-82
    DOI: 10.1016/j.amc.2016.04.011
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    Cited by:

    1. Suthep Suantai & Mana Donganont & Watcharaporn Cholamjiak, 2019. "Hybrid Methods for a Countable Family of G-Nonexpansive Mappings in Hilbert Spaces Endowed with Graphs," Mathematics, MDPI, vol. 7(10), pages 1-13, October.

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