关于p-一致光滑Banach空间中非自映像的Reich公开问题(英文)

On Reich's Open Problem on Nonself Mappings in p-Uniformly Smooth Banach Spaces

在p-一致光滑的Banach空间(1<p≤2)中,研究了非自映像的Reich公开问题,并在张(Nonlinear A-nalysis TMA,2007,66:2 364-2 374.)最近研究结果的基础上,作了如下的推广和改进:(1)把第一型修正的Reich序列推广到第一型带误差修正的Reich序列.(2)延拓算子的投影范围由自映象到非自映象.(3)去掉了原先的假设条件limn→∞an=0,∑∞在p-一致光滑的Banach空间(1<p≤2)中,研究了非自映像的Reich公开问题,并在张(Nonlinear A-nalysis TMA,2007,66:2 364-2 374.)最近研究结果的基础上,作了如下的推广和改进:(1)把第一型修正的Reich序列推广到第一型带误差修正的Reich序列.(2)延拓算子的投影范围由自映象到非自映象.(3)去掉了原先的假设条件li mn→∞an=0,∑∞n=0an=∞和∑∞n=0(kn-1)<∞.

We give an affirmative answer to the Reich＇s open problem in p-uniformly smooth Banaeh spaces （1 〈 p≤2）, and on the basis of the latest research results of Chang （Nonlinear Analysis TMA, 2007, 66：2 364-2 374）, we attain the following extending and improving： （1） Extend the iteration process from the primary first type of modified Reich sequence to the first type of modified Reich sequence with errors. （2） Enlarge the projection range of the mapping T from self-mapping to nonself-mapping. （3）Removethe primary assumptions liman n→∞=0,n=0∑an=∞ and n=0∑（kn-1）〈∞.