论文标题
量子MeyerKönig和Zeller-Fractal函数的近似
Approximation by Quantum Meyer König and Zeller-Fractal Functions
论文作者
论文摘要
在本文中，基于Meyer-König-Zeller操作员$ M_ {q，n} $引入了新的量子分形功能。这些量子Meyer-König-Zeller（MKZ）分形功能使用$ m_ {q，n} f $作为迭代功能系统中的基本函数，用于$α$ - fractal函数。对于$ f \在c（i）$中，$ i $以$ \ mathbb {r} $关闭，结果表明，存在一系列量子mkz分形函数$ \ {f^{（q_n，α，α，α）} _ n \} _ n \} _ { $ f^{（q_n，α）} _ n $的形状取决于$ q $以及其他IFS参数。 For $f,g\in C(I)$ with $g > 0$ or $f\geq g$, we show that there exists a sequence $\{f^{(q_n,α)}_n\}_{n=0}^{\infty}$ with $f^{(q_n,α)}_n \geq g$ converging to $f$.还提出了某些经典Müntz定理的量子MKZ分形版本。对于$ q = 1 $，在$ c（i）$中研究了MKZ $α$ fractal功能的盒子尺寸和一些近似理论结果。最后，以$ {p \ geq 1} $的$ l^p $空间研究MKZ $α$ - fractal功能。
In this paper, a novel class of quantum fractal functions is introduced based on the Meyer-König-Zeller operator $M_{q,n}$. These quantum Meyer-König-Zeller (MKZ) fractal functions employ $M_{q,n} f$ as the base function in the iterated function system for $α$-fractal functions. For $f\in C(I)$, $I$ closed in $\mathbb{R}$, it is shown that there exists a sequence of quantum MKZ fractal functions $\{f^{(q_n,α)}_n\}_{n=0}^{\infty}$ which converges uniformly to $f$ without altering the scaling function $α$. The shape of $f^{(q_n,α)}_n$ depends on $q$ as well as the other IFS parameters. For $f,g\in C(I)$ with $g > 0$ or $f\geq g$, we show that there exists a sequence $\{f^{(q_n,α)}_n\}_{n=0}^{\infty}$ with $f^{(q_n,α)}_n \geq g$ converging to $f$. Quantum MKZ fractal versions of some classical Müntz theorems are also presented. For $q=1$, the box dimension and some approximation-theoretic results of MKZ $α$-fractal function are investigated in $C(I)$. Finally, MKZ $α$-fractal functions are studied in $L^p$ spaces with ${p \geq 1}$.
