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

Sharma, S; Katiyar, K; Sudhamsu, G; Wratch, MK; Salgotra, R

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

Sharma, S Katiyar, K Sudhamsu, G Wratch, MK Salgotra, R

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Publisher:: MDPI
Publication Type:: Journal Article
Citation:: Axioms, 13, (9), pp. 584

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Field	Value	Language
dc.contributor.author	Sharma, S
dc.contributor.author	Katiyar, K
dc.contributor.author	Sudhamsu, G
dc.contributor.author	Wratch, MK
dc.contributor.author	Salgotra, R
dc.date.accessioned	2025-05-27T05:08:24Z
dc.date.available	2025-05-27T05:08:24Z
dc.identifier.citation	Axioms, 13, (9), pp. 584
dc.identifier.issn	2075-1680
dc.identifier.issn	2075-1680
dc.identifier.uri	http://hdl.handle.net/10453/187544
dc.description.abstract	<jats:p>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.</jats:p>
dc.language	en
dc.publisher	MDPI
dc.relation.ispartof	Axioms
dc.relation.isbasedon	10.3390/axioms13090584
dc.rights	info:eu-repo/semantics/restrictedAccess
dc.subject.classification	49 Mathematical sciences
dc.title	Positivity-Preserving Rational Cubic Fractal Interpolation Function Together with Its Zipper Form
dc.type	Journal Article
utslib.citation.volume	13
pubs.organisational-group	University of Technology Sydney
pubs.organisational-group	University of Technology Sydney/Faculty of Engineering and Information Technology
utslib.copyright.status	open_access	*
dc.date.updated	2025-05-27T05:08:22Z
pubs.issue	9
pubs.publication-status	Published online
pubs.volume	13
utslib.citation.issue	9

Abstract:

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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http://hdl.handle.net/10453/187544