凸度量空间内广义渐近拟非扩张映射不动点的迭代

Convergence of Ishikawa Type Iterative Sequence with Errors of Generalized Asymptotically Quasi-nonexpansive Mappings in Convex Metric Spaces

在凸度量空间中,引入一类比渐近拟非扩张映射更加广泛的广义渐近拟非扩张型映射,并给出带误差修改的Ishikawa迭代序列收敛于广义渐近拟非扩张型映射不动点的充要条件:设X是一个完备凸度量空间,T∶X→X是一个广义渐近拟非扩张型映射,其渐近系数kn满足∑∞n=1kn<+∞,并且F(T)非空。假定{xn}n∞=1是带误差修改的Ishikawa迭代序列,在对参数的一定限制下,{xn}n∞=1收敛于T的不动点,当且仅当lim infn→∞d(xn,F(T))=0。

In convex spaces this paper introduces a generalized asymptotically quasi-nonexpansive type mapping-a class of mapping, which is more general than asymptotic quasi-nonexpansive type mapping and gives some necessary and sufficient conditions for the Ish- ikawa iterative sequence with error to converge to a fixed point of generalized asymptotically quasi-nonexpansive type mapping in convex metric spaces： Let X is a complete convex metric space, T： X→X a generalized aasymptotically quasi-nonexpansive mappings , with ^∞∑n=1 kn〈＋∞ and F（T） nonempty. Suppose that {xn}n=1^∞ is the Ishikawa iterative process with erros, in the confine to scalars {xn}n=1^∞ converge to a fixed point of T, if and only if lim inf d n→∞（xn,F（T））=0.