A shape-preserving variant of Lane-Riesenfeld algorithm

Pakeeza Ashraf; Ghulam Mustafa; Husna A. Khan; Dumitru Baleanu; Abdul Ghaffar; Kottakkaran Sooppy Nisar; Pakeeza Ashraf; Ghulam Mustafa; Husna A. Khan; Dumitru Baleanu; Abdul Ghaffar; Kottakkaran Sooppy Nisar

doi:10.3934/math.2021131

AIMS Mathematics

2021, Volume 6, Issue 3: 2152-2170. doi: 10.3934/math.2021131

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Research article

A shape-preserving variant of Lane-Riesenfeld algorithm

1.
Department of Mathematics, Government Sadiq College Women University, Bahawalpur, Pakistan
2.
Department of Mathematics, The Islamia University of Bahawalpur, Pakistan
3.
Department of Mathematics, Cankaya University, Ankara, Turkey
4.
Institute of Space Sciences, 077125, Magurele-Bucharest, Romania
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40447, Taiwan
6.
School of Mathematics, Minhaj University Lahore, Pakistan
7.
Department of Mathematics, College of Arts and Sciences, Wadi Al-dawaser, Prince Sattam bin Abdulaziz University, 11991, Saudi Arabia

Received: 19 September 2020 Accepted: 25 November 2020 Published: 10 December 2020
MSC : 65D17, 65D15, 65D07, 65D05

This paper introduces a family of shape-preserving binary approximating subdivision schemes by applying a shape-preserving variant on the Lane-Riesenfeld algorithm. Using the symbols of subdivision schemes, we determine convergence and smoothness, Hölder continuity, and support size of the limit curves. Furthermore, these schemes produce monotonic and convex curves under the certain conditions imposed on the initial data.
- Lane-Riesenfeld algorithm,
- subdivision scheme,
- smoothness,
- shape preservation
Citation: Pakeeza Ashraf, Ghulam Mustafa, Husna A. Khan, Dumitru Baleanu, Abdul Ghaffar, Kottakkaran Sooppy Nisar. A shape-preserving variant of Lane-Riesenfeld algorithm[J]. AIMS Mathematics, 2021, 6(3): 2152-2170. doi: 10.3934/math.2021131

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Abstract

This paper introduces a family of shape-preserving binary approximating subdivision schemes by applying a shape-preserving variant on the Lane-Riesenfeld algorithm. Using the symbols of subdivision schemes, we determine convergence and smoothness, Hölder continuity, and support size of the limit curves. Furthermore, these schemes produce monotonic and convex curves under the certain conditions imposed on the initial data.

References

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