Banach空间中非扩张映象不动点的黏性逼近

Viscosity Approximtion of Fixed Points for Nonexpansive Mappings in Banach Spaces

中文关键词:  不动点  压缩映象  非扩张映象  黏性逼近.

英文关键词:fixed point  contractive mapping  nonexpansive mapping  viscosity approximation.

中文摘要:

      设$E$是一致光滑的Banach空间,其范数是一致Gateaux可微的;设$C$是$E$之一非空闭凸子集, $f:C\to C$是压缩映象, $T:C\to C$是非扩张映象.本文用黏性逼近方法证明了在较一般的条件下,由(1.6)式定义的迭代序列$\{x_n\}$的强收敛性.本文推广和改进了一些近期结果.

英文摘要:

      Let $E$ be a uniformly smooth Banach space, whose norm is uniformly Gateaux differentiable. Let $C$ be a closed convex subset of $E$, $f:C\rightarrow C$ be a contractive mapping, and $T:C\rightarrow C$ be a nonexpansive mapping. It is shown that under more general contractions of viscosity approximation methods, the sequence $\{x_n\}$ defined by (1.6) converges strongly. The results presented in this paper also extend and improve some recent results.