A generalization of Suzuki's lemma
Let {zn}, {wn}, and {vn} be bounded sequences in a metric space of hyperbolic type (X, d), and let {αn } be a sequence in [0,1] with 0 < lim infn αn < lim supnα n < 1. If zn+1=αnwn (1-α n)v n for all n ∈ ℕ , limnd (zn, v n) = 0, and lim supn(d (wn+1, wn) - d (zn+1, zn)) ≤ 0, the...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
2014
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| Online Access: | http://www.scopus.com/inward/record.url?eid=2-s2.0-80052686272&partnerID=40&md5=bff768eb5faed71904747e70152e3393 http://cmuir.cmu.ac.th/handle/6653943832/6459 |
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| Institution: | Chiang Mai University |
| Language: | English |
| Summary: | Let {zn}, {wn}, and {vn} be bounded sequences in a metric space of hyperbolic type (X, d), and let {αn } be a sequence in [0,1] with 0 < lim infn αn < lim supnα n < 1. If zn+1=αnwn (1-α n)v n for all n ∈ ℕ , limnd (zn, v n) = 0, and lim supn(d (wn+1, wn) - d (zn+1, zn)) ≤ 0, then limnd (w n, zn) = 0. This is a generalization of Lemma 2.2 in (T. Suzuki, 2005). As a consequence, we obtain strong convergence theorems for the modified Halpern iterations of nonexpansive mappings in CAT(0) spaces. Copyright © 2011 B. Panyanak and A. Cuntavepanit. |
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