On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures

Lal, Rattan; Selmi, Bilel; Verma, Saurabh

doi:10.1007/s00025-023-02108-w

Results Math

2024

DOI: 10.1007/s00025-023-02108-w

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On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures

Rattan Lal,

Bilel Selmi,

Saurabh Verma

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2024

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Cited by 3 publications

References 52 publications

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On α-fractal functions and their applications to analyzing the S&P BSE Sensex in India

Kumar,

Verma,

Boulaaras

2024

Chaos, Solitons & Fractals

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On α-fractal functions and their applications to analyzing the S&P BSE Sensex in India

Kumar,

Verma,

Boulaaras

2024

Chaos, Solitons & Fractals

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A note on fractal dimensions of graphs of certain continuous functions

Liu,

Yu,

Liang

2024

Chaos, Solitons & Fractals

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Positivity-Preserving Rational Cubic Fractal Interpolation Function Together with Its Zipper Form

Sharma,

Katiyar,

Sudhamsu

et al. 2024

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In this paper, a novel class of rational cubic fractal interpolation function (RCFIF) has been proposed, which is characterized by one shape parameter and a linear denominator. In interpolation for shape preservation, the proposed rational cubic fractal interpolation function provides a simple but effective approach. The nature of shape preservation of the proposed rational cubic fractal interpolation function makes them valuable in the field of data visualization, as it is crucial to maintain the original data shape in data visualization. Furthermore, we discussed the upper bound of error and explored the mathematical framework to ensure the convergence of RCFIF. Shape parameters and scaling factors are constraints to obtain the desired shape-preserving properties. We further generalized the proposed RCFIF by introducing the concept of signature, giving its construction in the form of a zipper-rational cubic fractal interpolation function (ZRCFIF). The positivity conditions for the rational cubic fractal interpolation function and zipper-rational cubic fractal interpolation function are found, which required a detailed analysis of the conditions where constraints on shape parameters and scaling factor lead to the desired shape-preserving properties. In the field of shape preservation, the proposed rational cubic fractal interpolation function and zipper fractal interpolation function both represent significant advancement by offering a strong tool for data visualization.

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On Dimension of Fractal Functions on Product of the Sierpiński Gaskets and Associated Measures

Cited by 3 publications

References 52 publications

On α-fractal functions and their applications to analyzing the S&P BSE Sensex in India

On α-fractal functions and their applications to analyzing the S&P BSE Sensex in India

A note on fractal dimensions of graphs of certain continuous functions

Positivity-Preserving Rational Cubic Fractal Interpolation Function Together with Its Zipper Form

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