湘潭大学自然科学学报
湘潭大學自然科學學報
상담대학자연과학학보
NATURAL SCIENCE JOURNAL OF XIANGTAN UNIVERSITY
2009年
4期
7-13
,共7页
非扩张映象%p-一致光滑%带误差的迭代逼近%不动点
非擴張映象%p-一緻光滑%帶誤差的迭代逼近%不動點
비확장영상%p-일치광활%대오차적질대핍근%불동점
nonexpansive mapping%p-uniformly smooth%iterative sequence with errors%fixed point
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 Analysis 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lim（X）n→∞an=0,∑∞n=0an=∞和∑∞n=0 (kn-1)<∞.
在p -一緻光滑的Banach空間(1<p≤2)中,研究瞭非自映像的Reich公開問題,併在張(Nonlinear Analysis TMA,2007,66:2 364-2 374.)最近研究結果的基礎上,作瞭如下的推廣和改進:（1）把第一型脩正的Reich序列推廣到第一型帶誤差脩正的Reich序列.（2）延拓算子的投影範圍由自映象到非自映象.（3）去掉瞭原先的假設條件lim（X）n→∞an=0,∑∞n=0an=∞和∑∞n=0 (kn-1)<∞.
재p -일치광활적Banach공간(1<p≤2)중,연구료비자영상적Reich공개문제,병재장(Nonlinear Analysis TMA,2007,66:2 364-2 374.)최근연구결과적기출상,작료여하적추엄화개진:（1）파제일형수정적Reich서렬추엄도제일형대오차수정적Reich서렬.（2）연탁산자적투영범위유자영상도비자영상.（3）거도료원선적가설조건lim（X）n→∞an=0,∑∞n=0an=∞화∑∞n=0 (kn-1)<∞.
We give an affirmative answer to the Reich's open problem in p-uniformly smooth Banach 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) Remove the primary assumptions lim(X)n→∞an=0,∑∞n=0an=∞ and ∑∞n=0 (kn-1)<∞.
