具误差隐格式迭代逼近严格伪压缩映像族公共不动点 (英)

设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset 0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset 0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset 0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设K是实Banach空间E中非空闭凸集，{Ti}i=1^N是N个具公共不动点集F的严格伪压缩映像，{αn}包括于0,1]是实数例，{un}包括于K是序列，且满足下面条件（i）0〈α≤αn≤1;（ii）∑n=1∞（1-αn）=＋∞.（iii）∑n=1∞ ‖un‖〈＋∞.设x0∈K,{xn}由正式定义xn=αnxn-1＋（1-αn）Tnxn＋un-1,n≥1,其中Tn=Tnmodn，则下面结论（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）lim infn→∞‖xn-Tnxn‖=0.文中另一个结果是，如果{xn}包括于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 $\{T_i\}_{i=1}^N$ be $N$ strictly pseudocontractive self-maps of $K$ such that $F=\bigcap_{i=1}^N F(T_i)\neq\emptyset$, where $F(T_i)=\{x \in K:T_ix=x\}$, $\{\alpha_n\}\subset 0,1]$ be a real sequence, and $\{u_n\}\subset K$ be a sequence satisfying the conditions: (i)~Let $E$ be a real Banach space and $K$ be a nonempty closed convex subset of $E$. Let $\{T_i\}_{i=1}^N$ be $N$ strictly pseudocontractive self-maps of $K$ such that $F=\bigcap_{i=1}^N F(T_i)\neq\emptyset$, where $F(T_i)=\{x \in K:T_ix=x\}$, $\{\alpha_n\}\subset 0,1]$ be a real sequence, and $\{u_n\}\subset K$ be a sequence satisfying the conditions: (i)~Let $E$ be a real Banach space and $K$ be a nonempty closed convex subset of $E$. Let $\{T_i\}_{i=1}^N$ be $N$ strictly pseudocontractive self-maps of $K$ such that $F=\bigcap_{i=1}^N F(T_i)\neq\emptyset$, where $F(T_i)=\{x \in K:T_ix=x\}$, $\{\alpha_n\}\subset 0,1]$ be a real sequence, and $\{u_n\}\subset K$ be a sequence satisfying the conditions: (i)~$0