Convergence of Ishikawa Type Iterative Sequence with Errors of Generalized Asymptotically Quasi-nonexpansive Mappings in Convex Metric Spaces
Wu Ting · Chongqing Shifan Daxue xuebao. Ziran kexue ban · 2007
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 Ishikawa 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=1kn+∞ and F(T)nonempty.Suppose that {xn}∞n=1is 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 infn→∞ d(xn,F(T))=0.