# Mathematical Communications,Vol.6 No.1 Lipanj 2001.

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Mann iteration for generalized pseudocontractive maps in Hilbert spaces

Ş. M. Şoltuz

 Puni tekst: engleski, pdf (72 KB) str. 97-100 preuzimanja: 395* citiraj APAŞoltuz, Ş.M. (2001). Mann iteration for generalized pseudocontractive maps in Hilbert spaces. Mathematical Communications, 6(1), 97-100. Preuzeto s http://hrcak.srce.hr/840

Sažetak
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.

Ključne riječi
Mann iteration; fixed points

Hrčak ID: 840

Posjeta: 540 *