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Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme

Author

Listed:
  • Pakeeza Ashraf

    (Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan)

  • Abdul Ghaffar

    (Informetrics Research Group, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam
    Faculty of Mathematics & Statistics, Ton Duc Thang University, Ho Chi Minh City 700000, Vietnam)

  • Dumitru Baleanu

    (Department of Mathematics, Cankaya University, Ankara 06530, Turkey
    Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
    Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40447, Taiwan)

  • Irem Sehar

    (Department of Mathematics, Government Sadiq College Women University, Bahawalpur 63100, Pakistan)

  • Kottakkaran Sooppy Nisar

    (Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia)

  • Faheem Khan

    (Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

Abstract

In this paper, we analyze shape-preserving behavior of a relaxed four-point binary interpolating subdivision scheme. These shape-preserving properties include positivity-preserving, monotonicity-preserving and convexity-preserving. We establish the conditions on the initial control points that allow the generation of shape-preserving limit curves by the four-point scheme. Some numerical examples are given to illustrate the graphical representation of shape-preserving properties of the relaxed scheme.

Suggested Citation

  • Pakeeza Ashraf & Abdul Ghaffar & Dumitru Baleanu & Irem Sehar & Kottakkaran Sooppy Nisar & Faheem Khan, 2020. "Shape-Preserving Properties of a Relaxed Four-Point Interpolating Subdivision Scheme," Mathematics, MDPI, vol. 8(5), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:5:p:806-:d:358511
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    References listed on IDEAS

    as
    1. Rehan, Kashif & Siddiqi, Shahid S., 2015. "A family of ternary subdivision schemes for curves," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 114-123.
    2. Siddiqi, Shahid S. & Noreen, Tayyaba, 2015. "Convexity preservation of six point C2 interpolating subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 936-944.
    3. Rehan, Kashif & Sabri, Muhammad Athar, 2016. "A combined ternary 4-point subdivision scheme," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 278-283.
    4. Sardar Muhammad Hussain & Aziz Ur Rehman & Dumitru Baleanu & Kottakkaran Sooppy Nisar & Abdul Ghaffar & Samsul Ariffin Abdul Karim, 2020. "Generalized 5-Point Approximating Subdivision Scheme of Varying Arity," Mathematics, MDPI, vol. 8(4), pages 1-25, March.
    Full references (including those not matched with items on IDEAS)

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