The inequalities for the analysis of a class of ternary refinement schemes

Ghulam Mustafa; Syeda Tehmina Ejaz; Dumitru Baleanu; Yu-Ming Chu; Ghulam Mustafa; Syeda Tehmina Ejaz; Dumitru Baleanu; Yu-Ming Chu

doi:10.3934/math.2020485

AIMS Mathematics

2020, Volume 5, Issue 6: 7582-7604. doi: 10.3934/math.2020485

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Research article

The inequalities for the analysis of a class of ternary refinement schemes

1.
Department of Mathematics, The Islamia University of Bahawalpur, Bahawalpur 63100, Pakistan
2.
Department of Mathematics, The Government Sadiq College Women University Bahawalpur, Bahawalpur 63100, Pakistan
3.
Department of Mathematics, Cankaya University, Ankara 06530, Turkey
4.
Institute of Space Sciences, 077125 Magurele-Bucharest, Romania
5.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
6.
Department of Mathematics, Huzhou University, Huzhou 313000, P. R. China
7.
Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science and Technology, Changsha 410114, P. R. China

Received: 04 July 2020 Accepted: 13 September 2020 Published: 24 September 2020
MSC : 65D17, 65D07, 65D05

The ternary refinement schemes are the generalized version of the binary refinement schemes. This class of the schemes produce the smooth curves with the less number of refinement steps as compared to the binary class of schemes. In this paper, we present the inequalities for the analysis of a class of ternary refinement schemes. There are three simple algebraic expressions in each inequality. Further these algebraic expressions contain only the coefficients used in the refinement rules of the ternary schemes.
- refinement scheme,
- binary,
- ternary,
- analysis,
- continuity,
- inequalities
Citation: Ghulam Mustafa, Syeda Tehmina Ejaz, Dumitru Baleanu, Yu-Ming Chu. The inequalities for the analysis of a class of ternary refinement schemes[J]. AIMS Mathematics, 2020, 5(6): 7582-7604. doi: 10.3934/math.2020485

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Abstract

The ternary refinement schemes are the generalized version of the binary refinement schemes. This class of the schemes produce the smooth curves with the less number of refinement steps as compared to the binary class of schemes. In this paper, we present the inequalities for the analysis of a class of ternary refinement schemes. There are three simple algebraic expressions in each inequality. Further these algebraic expressions contain only the coefficients used in the refinement rules of the ternary schemes.

References

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