Iterative Process to φ-Hemicontractive Operator and φ-Strongly Accretive Operator Equations
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摘要: 设E是任意实Banach空间,K是E的非空闭凸子集.T:K→K是一致连续φ-半压缩映像且值域有界.设{an},{bn},{cn},{a'n},{b'n}和{c'n}是[0,1]中的序列且满足条件:ⅰ)an+bn+cn=a'n+b'n+c'n=1,∀n≥0; 对任意给定的x0,u0,v0∈K,定义Ishikawa迭代{xn}如下:,其中un和vn是K中两个有界序列.则xn强收敛于T的唯一不动点.最后研究了φ-强增殖算子方程解的Ishikawa迭代收敛性.
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关键词:
- φ-强增殖算子 /
- φ-半压缩算子 /
- Ishikawa迭代序列 /
- Banach空间
Abstract: Let E be an arbitrary real Banach space and K be a nonempty closed convex subsets of E.Let T:K→K be a uniformly continuous φ-hemicontractive operator with bounded range and {an},{bn},{cn},{a'n},{b'n},{c'n}be sequences in[0,1] satisfying:ⅰ)an+bn+cn=a'n+b'n+c'n=1,∀n≥0; For any given x0,u0,v0∈K,define the Ishikawa type iterative sequence {xn} as follows: where {un} and {vn} are bounded sequences in K.Then {xn} converges strongly to the unique fixed point of T.Related result deals with the convergence of Ishikawa type iterative sequence to the solution of φ-strongly accretive operator equations. -
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