Original scientific paper
Mann iteration for generalized pseudocontractive maps in Hilbert spaces
Ş. M. Şoltuz
Abstract
If X is a real Hilbert space, B is a nonempty, bounded, convex and
closed subset, T:B→ B is a generalized pseudocontraction; then
the iteration
\begin{eqnarray}
x_{1} &\in &B, \\
x_{n+1} &=&(1-\alpha _{n})x_{n}+\alpha _{n}Tx_{n}, \nonumber \\
(\alpha _{n})_{n} &\subset &(0,1),\;\sum_{n=1}^{\infty }\alpha _{n}=\infty
,\; \nonumber \\
\sum_{n=1}^{\infty }\left| \alpha _{n+1}-\alpha _{n}\right| &<&\infty
,\;\lim_{n\rightarrow \infty }\alpha _{n}=0, \nonumber
\end{eqnarray}
strongly converges to the fixed point of T.
Keywords
Hrčak ID:
840
URI
Publication date:
20.6.2001.
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