A New Iterative Algorithm for Approximating Common Fixed Points for Asymptotically Nonexpansive Mappings
| Autor: | H. Y. Zhou, Y. J. Cho, S. M. Kang |
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| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: | |
| Zdroj: | Fixed Point Theory and Applications, Vol 2007 (2007) |
| Druh dokumentu: | article |
| ISSN: | 1687-1820 1687-1812 |
| DOI: | 10.1155/2007/64874 |
| Popis: | Suppose that K is a nonempty closed convex subset of a real uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction. Let T1,T2:K→E be two weakly inward and asymptotically nonexpansive mappings with respect to P with sequences {Kn},{ln}⊂[1,∞), limn→∞kn=1, limn→∞ln=1, F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠∅, respectively. Suppose that {xn} is a sequence in K generated iteratively by x1∈K, xn+1=αnxn+βn(PT1)nxn+γn(PT2)nxn, for all n≥1, where {αn}, {βn}, and {γn} are three real sequences in [ε,1−ε] for some ε>0 which satisfy condition αn+βn+γn=1. Then, we have the following. (1) If one of T1 and T2 is completely continuous or demicompact and ∑n=1∞(kn−1) |
| Databáze: | Directory of Open Access Journals |
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