Author/Authors :
RAZANI، A. نويسنده , , Salahifard، H. نويسنده Imam Khomeini International University ,
Abstract :
Let $C$ be a nonempty closed
convex subset of a complete $CAT(0)$ space and $T:C\to C$ be a
generalized nonexpansive mapping with $F(T)= \{x\in C:T(x)=x\}\neq
\emptyset$. Suppose $\{x_n\}$ is generated iteratively by $x_1 \in
C$,
\[
x_{n+1} = t_n T[s_n Tx_n \oplus (1- s_n)x_n]\oplus (1- t_n)x_n ,
\]
for all $ n\geq 1$, where $\{t_n\}$ and $\{s_n\}$ are real
sequences in $[0 ,1]$ such that one of the following two conditions is satisfied:\\
(i) $t_n \in [a,b]$ and $s_n \in [0,1]$, for some $a,b$ with $0 < a\leq b < 1$,\\
(ii) $t_n \in [a,1]$ and $s_n \in [a,b]$, for some $a,b$ with $0 < a\leq b < 1$.\\
Then, the sequence $\{x_n\}$, $\Delta$-converges to a fixed point
of $T$. Our results extend the ones in Laokul and Panyanak [{T.
Laokul and B. Panyanak, {\em Int. J. Math. Anal.} {\bf 3} (2009)
1305--1315.}] and also the ones in Nanjaras et al. [{B. Nanjaras,
B. Panyanak and W. Phuangrattana, {\em Nonlinear Anal. Hybrid
Syst.} {\bf 4} (2010) 25--31.}].
