|
|
|
|
|
Common fixed points and
iteration of commuting nonexpansive mappings
Shiro Ishikawa |
|
Vol. 80 (1979), No. 2, 493–501
|
Abstract |
|
The following result is shown. Let Ti (i = 1,2,⋯,ν) be commuting nonexpansive self-mappings on a compact convex subset D of a Banach space and let x be any point in D. Then the sequence ![n∏ν n∏ν−1 n∏2 ∏n1 ∞
{[ [Sν [⋅⋅⋅[S3 [S2 S1]]⋅⋅⋅]]]x}nν=1
nν−1=1 nν−2=1 n1=1 n0=1](a170x.png) converges to a common fixed point of {T}i=1ν, where Si = (1−αi)I +αiTi, 0 < αi < 1, I is the identity mapping. |
Mathematical Subject Classification 2000
Primary: 47H10
|
Milestones
Received: 30 May 1978
Published: 1 February 1979
|
Authors |
| Shiro Ishikawa | |
|
