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On the Bézier Variant of the Srivastava-Gupta Operators

Year 2018, , 99 - 107, 07.11.2018
https://doi.org/10.33205/cma.465073

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.

References

  • [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] 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] 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] 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] 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] 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] G. Chang, Generalized Bernstein-Bézier polynomials, J. Comput. Math. 1 (1983), No. 4, 322–327
  • [8] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer, New York 1987
  • [9] M. Goyal and P. N. Agrawal, Bézier variant of the Jakimovski-Leviatan-P˘alt˘anea operators based on Appell polynomials, Ann Univ Ferrara 63 (2017) 289-302
  • [10] M. Goyal and P. N. Agrawal, Bézier variant of the generalized Baskakov Kantorovich operators, Boll. Unione Mat. Ital. 8 (2016), 229-238
  • [11] V. Gupta, Some examples of genuine approximation operators, General Math. (2018) (in press)
  • [12] V. Gupta, Direct estimates for a new general family of Durrmeyer type operators, Boll. Unione Mat. Ital. 7 (2015) 279-288
  • [13] V. Gupta and R.P. Agarwal, Convergence Estimates in Approximation Theory, Springer, 2014
  • [14] V. Gupta, On the Bézier variant of Kantorovich operators, Comput. Math. Anal. 47 (2004), 227–232
  • [15] S. Guo, Q. Qi and G. Liu, The central theorems for Baskakov-Bézier operators, J. Approx. Theory 147 (2007), 112–124
  • [16] N. Ispir and I. Yuksel, On the Bézier variant of Srivastava-Gupta operators, Appl. Math. E-Notes, 5 (2005), 129-137
  • [17] A. Kajla and T. Acar, A new modification of Durrmeyer type mixed hybrid operators, Carpathian J. Math. 34 (2018) 47-56
  • [18] T. Neer, N. Ispir and P. N. Agrawal, Bézier variant of modified Srivastava-Gupta operators, Revista de la Union Matematica Argentina, 58 (2017) 199-214
  • [19] H. M. Srivastava, Z. Finta and V. Gupta, Direct results for a certain family of summation-integral type operators, Appl. Math. Comput. 190 (2007) 449-457.
  • [20] H. M. Srivastava and V. Gupta, Rate of convergence for the Bézier variant of the Bleimann-Butzer-Hahn operators, Appl. Math. Lett. 18 (2005), 849–857
  • [21] H. M. Srivastava and X.M. Zeng, Approximation by means of the Szász-Bézier integral operators, International J. Pure Appl. Math. 14 (2004), No. 3, 283–294
  • [22] R. Yadav, Approximation by modified Srivastava-Gupta operators, Appl. Math. Comput. 226 (2014), 61-66
  • [23] D. K. Verma and P. N. Agrawal, Convergence in simultaneous approximation for Srivastava-Gupta operators, Math. Sci., 2012, 6-22
  • [24] X.M. Zeng, On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions II, J. Approx. Theory 104 (2000), 330–344
  • [25] X. M. Zeng and A. Piriou, On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions, J. Approx. Theory 95 (1998), 369–387
  • [26] X. M. Zeng andW. Chen, On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation, J. Approx. Theory 102 (2000), 1–12
Year 2018, , 99 - 107, 07.11.2018
https://doi.org/10.33205/cma.465073

Abstract

References

  • [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] 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] 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] 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] 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] 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] G. Chang, Generalized Bernstein-Bézier polynomials, J. Comput. Math. 1 (1983), No. 4, 322–327
  • [8] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer, New York 1987
  • [9] M. Goyal and P. N. Agrawal, Bézier variant of the Jakimovski-Leviatan-P˘alt˘anea operators based on Appell polynomials, Ann Univ Ferrara 63 (2017) 289-302
  • [10] M. Goyal and P. N. Agrawal, Bézier variant of the generalized Baskakov Kantorovich operators, Boll. Unione Mat. Ital. 8 (2016), 229-238
  • [11] V. Gupta, Some examples of genuine approximation operators, General Math. (2018) (in press)
  • [12] V. Gupta, Direct estimates for a new general family of Durrmeyer type operators, Boll. Unione Mat. Ital. 7 (2015) 279-288
  • [13] V. Gupta and R.P. Agarwal, Convergence Estimates in Approximation Theory, Springer, 2014
  • [14] V. Gupta, On the Bézier variant of Kantorovich operators, Comput. Math. Anal. 47 (2004), 227–232
  • [15] S. Guo, Q. Qi and G. Liu, The central theorems for Baskakov-Bézier operators, J. Approx. Theory 147 (2007), 112–124
  • [16] N. Ispir and I. Yuksel, On the Bézier variant of Srivastava-Gupta operators, Appl. Math. E-Notes, 5 (2005), 129-137
  • [17] A. Kajla and T. Acar, A new modification of Durrmeyer type mixed hybrid operators, Carpathian J. Math. 34 (2018) 47-56
  • [18] T. Neer, N. Ispir and P. N. Agrawal, Bézier variant of modified Srivastava-Gupta operators, Revista de la Union Matematica Argentina, 58 (2017) 199-214
  • [19] H. M. Srivastava, Z. Finta and V. Gupta, Direct results for a certain family of summation-integral type operators, Appl. Math. Comput. 190 (2007) 449-457.
  • [20] H. M. Srivastava and V. Gupta, Rate of convergence for the Bézier variant of the Bleimann-Butzer-Hahn operators, Appl. Math. Lett. 18 (2005), 849–857
  • [21] H. M. Srivastava and X.M. Zeng, Approximation by means of the Szász-Bézier integral operators, International J. Pure Appl. Math. 14 (2004), No. 3, 283–294
  • [22] R. Yadav, Approximation by modified Srivastava-Gupta operators, Appl. Math. Comput. 226 (2014), 61-66
  • [23] D. K. Verma and P. N. Agrawal, Convergence in simultaneous approximation for Srivastava-Gupta operators, Math. Sci., 2012, 6-22
  • [24] X.M. Zeng, On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions II, J. Approx. Theory 104 (2000), 330–344
  • [25] X. M. Zeng and A. Piriou, On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions, J. Approx. Theory 95 (1998), 369–387
  • [26] X. M. Zeng andW. Chen, On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation, J. Approx. Theory 102 (2000), 1–12
There are 26 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Arun Kajla

Publication Date November 7, 2018
Published in Issue Year 2018

Cite

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