MHB Understanding Picard Iteration: What Does ${f}^{n}x \subseteq {f}^{n+1}x$ Mean?

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The discussion centers on the meaning of the notation ${f}^{n}x \subseteq {f}^{n+1}x$ in the context of Picard iteration, specifically regarding the Picard operator $T$. Participants clarify that $x_n = T{x}^{n-1}$ represents functions acted upon by the Picard operator. There is confusion about the meaning of the $f^n$ symbols, which are not clearly defined in the initial query. A link to a resource is provided for further context, specifically pointing to page 5 of a referenced document. Understanding these concepts is crucial for grasping the implications of Picard iteration in mathematical analysis.
ozkan12
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İn some articles...I see something... Let ${x}_{n}=T{x}^{n-1}$ be a Picard Operator...Then ${f}^{n}x \subseteq {f}^{n+1}x$...What is the meaning of this ? Can you help me ?
 
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You need to give just a bit more context, please. So far, $T$ is the Picard operator; Picard operators act on functions, so the $x_n$ are functions. But I have no idea what the $f^n$ symbols mean.
 

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