{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2024,8,29]],"date-time":"2024-08-29T00:29:19Z","timestamp":1724891359248},"reference-count":52,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T00:00:00Z","timestamp":1724803200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"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.<\/jats:p>","DOI":"10.3390\/axioms13090584","type":"journal-article","created":{"date-parts":[[2024,8,28]],"date-time":"2024-08-28T07:57:06Z","timestamp":1724831826000},"page":"584","source":"Crossref","is-referenced-by-count":0,"title":["Positivity-Preserving Rational Cubic Fractal Interpolation Function Together with Its Zipper Form"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"http:\/\/orcid.org\/0009-0002-1606-4589","authenticated-orcid":false,"given":"Shamli","family":"Sharma","sequence":"first","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, India"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-9772-4026","authenticated-orcid":false,"given":"Kuldip","family":"Katiyar","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Chandigarh University, Gharuan, Mohali 140413, Punjab, India"}]},{"given":"Gadug","family":"Sudhamsu","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, School of Engineering and Technology, JAIN (Deemed to be University), Bangalore 560069, Karnataka, India"}]},{"given":"Manjinder Kaur","family":"Wratch","sequence":"additional","affiliation":[{"name":"Department of Computer Science Engineering, Chandigarh Engineering College, Chandigarh Group of Colleges, Jhanjeri, Mohali 140307, Punjab, India"}]},{"ORCID":"http:\/\/orcid.org\/0000-0002-3282-1810","authenticated-orcid":false,"given":"Rohit","family":"Salgotra","sequence":"additional","affiliation":[{"name":"Faculty of Physics and Applied Computer Science, AGH University of Krakow, 30-059 Krakow, Poland"},{"name":"MEU Research Unit, Middle East University, Amman 11813, Jordan"},{"name":"Data Science Institute, University of Technology Sydney, Sydney, NSW 2007, Australia"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"340","DOI":"10.1007\/BF01934097","article-title":"Positivity of cubic polynomials on intervals and positive spline interpolation","volume":"28","author":"Schmidt","year":"1988","journal-title":"BIT Numer. 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