Strong convergence theorems for asymptotically k-strictly pseudocontractive maps
 作者： E.E. Chima,  M.O. Osilike,  S.E. Odibo,  R.Z. Nwoha,  P.U. Nwokoro,  D.F. Agbebaku 作者单位： 1Bingham University, Karu,Nigeria 刊名： Advances in Fixed Point Theory, 2019, Vol.9 (2), pp.178-205 来源数据库： Science & Knowledge Publishing Corporation Limited 原始语种摘要： Let $C$ be a nonempty closed convex subset of a real Hilbert space, $H$ and let $T: C \rightarrow C$ be an asymptotically $k$-strictly pseudo-contractive mapping with a nonempty fixed-point set, $F(T)=\{x\in C: Tx=x\}$. Let $\{t_n\}$, $\lbrace\alpha_{n}\rbrace$~ and $\lbrace\beta_{n}\rbrace$~ be real ~sequences in $( 0, 1)$. We consider the sequence $\lbrace x_{n}\rbrace$, ge nerated from an arbitrary $x_{1} \in C$, by either I. \hskip 3.0cm $x_{n+1} = P_C[\left( 1-\alpha_{n} - \beta_{n}\right) x_{n}+ \beta_{n}T^{n}x_{n}], \; n\geq 1,$ or II. $\left\{\begin{array}{ll} \nu_n=P_C((1-t_n)x_n) x_{n+1}=(1-\alpha_n)\nu_n+\alpha_nT^n\nu_n, \; n\geq 1\end{array}\right.$ We prove that under some mild conditions on the real sequences $\lbrace\alpha_{n}\rbrace$ and $\lbrace\beta_{n}\rbrace$, the... sequence $\lbrace x_{n}\rbrace$ generated by I converges strongly to a fixed point of $T$. Furthermore, under some mild conditions on the sequences $\{t_n\}$ and $\{\alpha_n\}$, the sequence generated by II converges strongly to the least norm element of the fixed point set of $T$. Some examples are used to compare the convergence rates of these two iteration schemes. Our results compliment and extend several strong convergence results in the literature to the class of mappings considered in our work.

• asymptotically　渐近地
• strictly　严密地
• convergence　汇合
• strongly　强烈地
• contractive　收缩的
• fixed　固定
• nonempty　非空的
• iteration　迭代
• alpha　接字母顺序的
• right　右边的