On δ-convergence of the Ishikawa iterative process for nonexpansive mappings in cat(0) spaces
Let C be a nonempty closed convex subset of a complete CAT(0) space and T: C → C be a nonexpansive mapping with a fixed point. Suppose that {xn} is defined by x1 ∈ C and xn+1 = tnT[snTxn ⊕ (1-sn)xn] ⊕ (1-tn)xn for all n ≥ 1, where {tn} and {sn} are sequences in [0, 1] such that one of the following...
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| Main Authors: | , |
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| Format: | Article |
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Yokohama Publishers
2015
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| Online Access: | http://www.scopus.com/inward/record.url?partnerID=HzOxMe3b&scp=84894127839&origin=inward http://cmuir.cmu.ac.th/handle/6653943832/38714 |
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| Institution: | Chiang Mai University |
| Summary: | Let C be a nonempty closed convex subset of a complete CAT(0) space and T: C → C be a nonexpansive mapping with a fixed point. Suppose that {xn} is defined by x1 ∈ C and xn+1 = tnT[snTxn ⊕ (1-sn)xn] ⊕ (1-tn)xn for all n ≥ 1, where {tn} and {sn} are sequences in [0, 1] such that one of the following two conditions is satisfied: (i)∑∞ n=1 tn (1-tn) = ∞ and lim suptn stn < 1; (ii)∑∞ n=1 tn sn = ∞ and lim supn sn ≤ 1: Then the sequence {xn} δ-converges to a fixed point of T: This is an analog of a result in Banach spaces of Suzuki and Takahashi [29] and generalizes some results in [10] and [22]. © 2010 yokohama publishers. |
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