摘要
Ｌｅｍｍａ１［１］ＩｆＥｉｓａｕｎｉｆｏｒｍｌｙｓｍｏｏｔｈＢａｎａｃｈｓｐａｃｅ，ｔｈｅｒｅｅｘｉｓｔｓａｃｏｎｔｉｎｕｏｕｓｎｏｎｄｅｃｒｅａｓｉｎｇｆｕｎｃｔｉｏｎβ（ｔ）：［０，∞）→［０，∞）ｓｕｃｈｔｈａｔｌｉｍｔ→０＋β（ｔ）＝０，β...
Let E be a real uniformly smooth Banach space and let K be a nonempty closed convex and bounded subset of E . Let T: K→K be a strict hemi contraction mapping, that is, F(T)={x|Tx=x}≠ and there exists t>1 such that‖x-x *‖≤‖(1+r)(x-x *)-rt(Tx-x *)‖for all x∈K, x *∈F(T) and r>0 . Let {α n} ∞ n=0 and {β n} ∞ n=0 be two real sequences satisfying: (i) 0≤α n, β n≤1 for all nonnegative integer n , (ii) lim n→∞α n=0 and lim n→∞β n=0 , (iii) ∑∞n=0α n=∞ . For arbitrary x 0∈K , define the sequence {x n} ∞ n=1 in K byx n+1 =(1-α n)x n+α nTy n y n=(1-β n)x n+β nTx nThen the sequence {x n} ∞ n=1 converges strongly to the unique fixed point of T .
出处
《西南师范大学学报（自然科学版）》
CAS
CSCD
北大核心
1998年第5期7-10,共4页
Journal of Southwest China Normal University(Natural Science Edition)
