On the Bézier Variant of the Srivastava-Gupta Operators
On the Bézier Variant of the Srivastava-Gupta Operators
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.
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- [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