具误差隐格式迭代逼近严格伪压缩映像族公共不动点

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．

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

Let E be a real Banach space and K be a nonempty closed convex subset of E.Let {Ti}iN=1 be N strictly pseudocontractive self-maps of K such that F=∩Ni=1 F(Ti)≠φ,where F(Ti)={x∈K:Tix=x},{an}(∩)0,1] be a real sequence,and {un}(∩)K be a sequence satisfying the conditions:(i)0＜a≤an≤1;(ii)∑n∞=1(1-an)=+∞;(iii)∑n∞=1⊥‖un‖＜+∞.Let xo ∈K and {xn}n∞=1 be defined by xn=anxn-1+(1-an)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{an}∞n=1(∩)1-2-n,1],then {xn} is convergent. This paper generalizes and improves the results of Osilike in 2004.The ideas and.proof fines used in this paper are different from those of Osilike in 2004.