A New Class of 2 q -Point Nonstationary Subdivision Schemes and Their Applications

Abdul Ghaffar, Mehwish Bari, Zafar Ullah, Mudassar Iqbal, Kottakkaran Sooppy Nisar and Dumitru Baleanu
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Abdul Ghaffar: Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
Mehwish Bari: Department of Mathematics, NCBA&E, Bahawalpur 63100, Pakistan
Zafar Ullah: Department of Mathematics, University of Education Lahore, Campus DG Khan, Dera Ghazi Khan 54770, Pakistan
Mudassar Iqbal: Department of Mathematical Sciences, BUITEMS, Quetta 87300, Pakistan
Kottakkaran Sooppy Nisar: Department of Mathematics, College of Arts and Sciences, Prince Sattam bin Abdulaziz University, Wadi Aldawaser 11991, Saudi Arabia
Dumitru Baleanu: Department of Mathematics, Cankaya University, Ankara 06530, Turkey

Mathematics, 2019, vol. 7, issue 7, 1-21

Abstract: The main objective of this study is to introduce a new class of 2 q -point approximating nonstationary subdivision schemes (ANSSs) by applying Lagrange-like interpolant. The theory of asymptotic equivalence is applied to find the continuity of the ANSSs. These schemes can be nicely generalized to contain local shape parameters that allow the user to locally adjust the shape of the limit curve/surface. Moreover, many existing approximating stationary subdivision schemes (ASSSs) can be obtained as nonstationary counterparts of the proposed ANSSs.

Keywords: stationary; nonstationary; subdivision scheme; continuity; curvature and torsion (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
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