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Title of Journal: Optim Lett

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Abbravation: Optimization Letters

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Springer Berlin Heidelberg

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DOI

10.1016/0378-4371(92)90176-q

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1862-4480

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Strong convergence of Mann’s type iteration method

Authors: WeiQi Deng
Publish Date: 2012/12/05
Volume: 8, Issue: 2, Pages: 533-542
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Abstract

Let C be a nonempty closed convex subset of a real Hilbert space H Let T iinfty i=1Crightarrow H be an infinite family of generalized asymptotically nonexpansive nonself mappings By using a specific way of choosing the indexes of the involved mappings we prove strong convergence of Mann’s type iteration to a common fixed point of T iinfty i=1 without the compactness assumption imposed either on T or on C provided that the interior of common fixed points is nonempty The results extend previous results restricted to the situation of at most finite families of such mappings

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