Mann迭代和具误差的Ishikawa迭代收敛性的等价定理  

Equivalence theorems of the convergence between Mann iteration and Ishikawa iteration with errors

作　　者：倪仁兴[1] 

机构地区：[1]绍兴文理学院数学系,浙江绍兴312000

出　　处：《高校应用数学学报（A辑）》2010年第3期359-364,共6页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金(10971194);浙江省自然科学基金(Y606717)

摘　　要：在迭代参数仅满足(?) supβ_n<(k/L(L+1)),(?)α_n=0和(?)α_n=+∞的条件下,用不同与于已有的方法证明了任意实Banach空间中的Lipschitz强伪压缩算子的Mann迭代和具误差的Ishikawa迭代收敛是等价的.这推广和改进了目前需假设limβ_n=0和两迭代程序的初始点的取值需相同条件下的已知结果.Let T be a Lipschitzian strongly pseudo-contractive operator in an arbitrary real Bak nach space. Assume that the iteration parameters satisfy conditionslimn→supβn〈k/L（L＋1）,limn→∞an=0and＋∞∑n=0an=＋∞ It is proved that certain Mann iteration and Ishikawa iterative schemes with errors are equivalent. These results generalize and extend the results which need conditions limn→∞βn=0 and the initial points of two different iterations are the same one.

关 键 词：强伪压缩算子 MANN迭代 具误差的Ishikawa迭代 等价定理 收敛性 

分 类 号：O177.91[理学—数学]