Research Article

On the Bézier Variant of the Srivastava-Gupta Operators

Volume: 1 Number: 2 November 7, 2018
EN

On the Bézier Variant of the Srivastava-Gupta Operators

Abstract

In the present paper, we introduce the Bézier variant of the Srivastava-Gupta operators, which preserve constant as well as linear functions. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness, respectively the rate of convergence for differentiable functions whose derivatives are of bounded variation.

Keywords

References

  1. [1] U. Abel and V. Gupta, An estimate of the rate of convergence of a Bézier variant of the Baskaokov-Kantorovich operators for bounded variation functions, Demonstratio Math. 36 (2003), No. 1, 123–136
  2. [2] T. Acar and A. Kajla, Blending type approximation by Bézier-summation-integral type operators, Commun. Fac. Sci., Univ. Ank. Ser. A1 Math. Stat. 66 (2018), No. 2, 195–208
  3. [3] T. Acar, L. N. Mishra and V. N. Mishra, Simultaneous approximation for generalized Srivastava-Gupta operators, J. Funct. Spaces 2015, Article ID 936308, 11 pages.
  4. [4] T. Acar, P. N. Agrawal and T. Neer, Bézier variant of the Bernstein-Durrmeyer type operators, Results. Math., DOI: 10.1007/s00025-016-0639-3.
  5. [5] P. N. Agrawal, S. Araci, M. Bohner and K. Lipi, Approximation degree of Durrmeyer -Bézier type operators, J. Inequal. Appl. (2018), Doi:10.1186/s13660-018-1622-1
  6. [6] P. N. Agrawal, N. Ispir and A. Kajla, Approximation properties of Bézier-summation-integral type operators based on Polya-Bernstein functions, Appl. Math. Comput. 259 (2015), 533–539
  7. [7] G. Chang, Generalized Bernstein-Bézier polynomials, J. Comput. Math. 1 (1983), No. 4, 322–327
  8. [8] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer, New York 1987

Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Publication Date

November 7, 2018

Submission Date

September 28, 2018

Acceptance Date

October 17, 2018

Published in Issue

Year 2018 Volume: 1 Number: 2

APA
Kajla, A. (2018). On the Bézier Variant of the Srivastava-Gupta Operators. Constructive Mathematical Analysis, 1(2), 99-107. https://doi.org/10.33205/cma.465073
AMA
1.Kajla A. On the Bézier Variant of the Srivastava-Gupta Operators. CMA. 2018;1(2):99-107. doi:10.33205/cma.465073
Chicago
Kajla, Arun. 2018. “On the Bézier Variant of the Srivastava-Gupta Operators”. Constructive Mathematical Analysis 1 (2): 99-107. https://doi.org/10.33205/cma.465073.
EndNote
Kajla A (November 1, 2018) On the Bézier Variant of the Srivastava-Gupta Operators. Constructive Mathematical Analysis 1 2 99–107.
IEEE
[1]A. Kajla, “On the Bézier Variant of the Srivastava-Gupta Operators”, CMA, vol. 1, no. 2, pp. 99–107, Nov. 2018, doi: 10.33205/cma.465073.
ISNAD
Kajla, Arun. “On the Bézier Variant of the Srivastava-Gupta Operators”. Constructive Mathematical Analysis 1/2 (November 1, 2018): 99-107. https://doi.org/10.33205/cma.465073.
JAMA
1.Kajla A. On the Bézier Variant of the Srivastava-Gupta Operators. CMA. 2018;1:99–107.
MLA
Kajla, Arun. “On the Bézier Variant of the Srivastava-Gupta Operators”. Constructive Mathematical Analysis, vol. 1, no. 2, Nov. 2018, pp. 99-107, doi:10.33205/cma.465073.
Vancouver
1.Arun Kajla. On the Bézier Variant of the Srivastava-Gupta Operators. CMA. 2018 Nov. 1;1(2):99-107. doi:10.33205/cma.465073

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