Approximation by Quantum Meyer König and Zeller-Fractal Functions Article Swipe

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D. Kumar , A. K. B. Chand , Peter Massopust ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2210.11163

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 ${p \geq 1}$.

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Iterated function system Fractal Quantum Iterated function Mathematics Sequence (biology) Function (biology) Combinatorics Scaling Operator (biology) Mathematical physics Physics Mathematical analysis Quantum mechanics Geometry Genetics Gene Chemistry Biology Evolutionary biology Transcription factor Repressor Biochemistry

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2210.11163
PDF: https://arxiv.org/pdf/2210.11163
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DOI: https://doi.org/10.48550/arxiv.2210.11163

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Title: Approximation by Quantum Meyer König and Zeller-Fractal Functions

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Language: en

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Publication year: 2022

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Publication date: 2022-10-20

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Authors: D. Kumar, A. K. B. Chand, Peter Massopust

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Concepts: Iterated function system, Fractal, Quantum, Iterated function, Mathematics, Sequence (biology), Function (biology), Combinatorics, Scaling, Operator (biology), Mathematical physics, Physics, Mathematical analysis, Quantum mechanics, Geometry, Genetics, Gene, Chemistry, Biology, Evolutionary biology, Transcription factor, Repressor, Biochemistry

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