具误差隐格式迭代逼近严格伪压缩映像族公共不动点  

Implicit Iteration Process with Errors for Common Fixed Points of a Finite Family of Strictly Pseudo contractive Maps

作　　者：苏永福[1] 李素红[1] 宋义生[1] 周海云[2] 

机构地区：[1]天津工业大学理学院数学系,天津300160 [2]石家庄军械工程学院数学系,河北石家庄050003

出　　处：《Journal of Mathematical Research and Exposition》2007年第1期98-106,共9页数学研究与评论（英文版）

基　　金：the National Natural Science Foundation of China(10471033);Tianjin Construction of Course(100580204).

摘　　要：设K是实Banach空间E中非空闭凸集, {Ti}i=1N是N个具公共不动点集F的严格伪压缩映像, {an}(?)[0,1]是实数列, {un}(?)K是序列,且满足下面条件设X0∈K,{xn}由下式定义xn=αnxn-1+(1-αn)Tnxn-un-1,n≥1其中Tn=TnmodN,则有下面结论(i)limn→∞‖xn-p‖存在,对所有P∈F; (ii)limn→∞d(xn,F)存在,当d(xn,F)=infp∈F‖xn-p‖; (iii)liminfn→∞‖xn-Tnxn‖=0．文中另一个结果是,如果{xn}(?){1-2-n,1},则{xn}收敛．文中结果改进与扩展了Osilike(2004)最近的结果,证明方法也不同．Let E be a real Banach space and K be a nonempty closed convex subset of E. Let {Ti}i=1^N be N strictly pseudocontractive self-maps of K such that F =∩i=1^NF（Ti）≠φ ,where F（Ti）={x∈k：Tix=x},{αn}lohtain in [0,1] be a real sequence,and {un} lohtain in Kbe a sequence satisfying the conditions：（i）0〈α≤αn≤1;（ii）∑n=1∞（1-αn）=＋∞.（iii）∑n=1∞ ‖un‖〈＋∞.Let x0∈K and {xn}n=1^∞ be defined by xn=αnxn-1＋（1-αn）Tnxn＋un-1,n≥1,where Tn=Tnmodn,then（i）limn→∞‖xn-p‖exists for all p∈F;（ii）limn→∞d（xn,F）exists,where d（xn,F）=infp∈F‖xn-p‖;（iii）lim infn→∞‖xn-Tnxn‖=0.Another result is that if {αn}n=1∞ loghtain in [1-2^-n,1], then {xn} is convergent. This paper generalizes and improves the results of Osilike in 2004. The ideas and proof lines used in this paper are different from those of Osilike in 2004.

关 键 词：严格伪压缩映像 具误差隐格式迭代 公共不动点 收敛定理 

分 类 号：O177.91[理学—数学]