Successive approximations for common fixed points of a family of α -nonexpansive mappings
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Author list: Song Y., Muangchoo-in K., Kumam P., Cho Y.J.
Publisher: Springer
Publication year: 2018
Journal: Journal of Fixed Point Theory and Applications (1661-7738)
Volume number: 20
Issue number: 1
ISSN: 1661-7738
eISSN: 1661-7746
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, we consider the Halpern iteration for α-nonexpansive mapping semigroups; such semigroups contain classical nonexpansive mapping semigroups as special cases. The strong convergence theorems of Halpern iteration sequence are shown for finding a common fixed point of an α-nonexpansive semigroup, which exactly is a metric projection point of the anchor point u to the common fixed point set of such semigroups. Furthermore, the strong convergence of the Halpern iteration for an α-nonexpansive mapping sequence is given also. © 2018, Springer International Publishing AG, part of Springer Nature.
Keywords
Iteration, Semigroup of mappings
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