Banach空间中伪压缩映象不动点的迭代逼近

Let K be a nonempty closed convex subset of a real p-uniformly convex Banach space E and T be a Lipschitz pseudocontractive self-mapping of K with F（T） ：= {x ∈ K：Tx=x}≠φ. Let a sequence {xn} be generated from x1 ∈ K by xn＋1 = anxn,＋ bnTyn＋＋ cnun, yn= a′nxn~ ＋ b′nTx,＋ c′n,un, for all integers n ≥ 1. Then ‖xn - Txn,‖ → 0 as n→∞. Moreover, if T is completely continuous, then {xn} converges strongly to a fixed point of T.

Approximating Fixed Points of Pseudocontractive Mapping in Banach Spaces

Let $K$ be a nonempty closed convex subset of a real p-uniformly convex Banach space $E$ and $T$ be a Lipschitz pseudocontractive self-mapping of $K$ with $F(T):={xin K: Tx=x}neq emptyset$. Let a sequence ${x_n}$ be generated from $x_1in K$ by $x_{n+1}=a_nx_n+b_nTy_n+c_nu_n$, $y_n=a'_nx_n+b'_nTx_n+c^{'}_nv_n$ for all integers $ngeq 1$. Then $|x_n-Tx_n|rightarrow 0$ as $nrightarrow infty$. Moreover, if $T$ is completely continuous, then ${x_n}$ converges strongly to a fixed point of $T$.