Inhomogeneous iterates and nonlinear weak ergodic theorems. (Q2753304)
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scientific article; zbMATH DE number 1667858
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Inhomogeneous iterates and nonlinear weak ergodic theorems. |
scientific article; zbMATH DE number 1667858 |
Statements
26 September 2002
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weakly ergodic sequence
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generalized contraction
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Inhomogeneous iterates and nonlinear weak ergodic theorems. (English)
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A sequence \(T_n\) of functions defined on a subset \(S\) of a Banach space \(B\) is called weakly ergodic, if for all \(x,y\in S\), NEWLINE\[NEWLINE\lim_{n\to\infty}\,\| T_n\circ\cdots\circ T_1(x)- T_n\circ\cdots\circ T_1(y)\|= 0.NEWLINE\]NEWLINE The author proves several weak ergodic theorems for maps \(T_n\) which leave a certain cone \(S\) invariant and arise from linear operators \(f_n\) by rescaling: \(T_n= {f_n\over\| f_n\|}\).NEWLINENEWLINEFor the entire collection see [Zbl 0969.00060].
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