Iterative Approximation of Common Fixed Points of Two Nonself Asymptotically Nonexpansive Mappings
Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F:=F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠∅. Let T1,T2:K→E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences {kn(i)}...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2011-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2011/487864 |
| Summary: | Suppose that K is nonempty closed convex subset of a uniformly convex and smooth Banach space E with P as a sunny nonexpansive retraction and F:=F(T1)∩F(T2)={x∈K:T1x=T2x=x}≠∅. Let T1,T2:K→E be two weakly inward nonself asymptotically nonexpansive mappings with respect to P with two sequences {kn(i)}⊂[1,∞) satisfying ∑n=1∞(kn(i)-1)<∞(i=1,2), respectively. For any given x1∈K, suppose that {xn} is a sequence generated iteratively by xn+1=(1-αn)(PT1)nyn+αn(PT2)nyn, yn=(1-βn)xn+βn(PT1)nxn, n∈N, where {αn} and {βn} are sequences in [a,1-a] for some a∈(0,1). Under some suitable conditions, the strong and weak convergence theorems of {xn} to a common fixed point of T1 and T2 are obtained. |
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| ISSN: | 1026-0226 1607-887X |