Strong convergence theorems for asymptotically k-strictly pseudocontractive maps
作者: E.E. ChimaM.O. OsilikeS.E. OdiboR.Z. NwohaP.U. NwokoroD.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...
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  • 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