Rate of Convergence for Generalized Baskakov-Durrmeyer Operators

In the present paper, we consider the generalized form of Baskakov Durrmeyer operators to study the rate of convergence, in simultaneous approximation for functions having derivatives of bounded variation.

• Durvesh Kumar Verma
• P. N. Agrawal

• Bounded variation
• Baskakov-Durrmeyer operators
• simultaneous approximation
• rate of convergence.

[1] G. D. Bai, Y.H. Hua, S.Y. Shaw, Rate of approximation for functions with
derivatives of bounded variation, Anal. Math. 28 (3) (2002), 171-196.
[2] Z. Finta, On converse approximation theorems, J. Math. Anal. Appl., 312
(1) (2005), 159-180.
[3] N. K. Govil and V. Gupta, Direct estimates in simultaneous approximation
for Durrmeyer type operators, Math. Ineq. Appl., 10 (2) (2007), 371-379.
[4] V. Gupta, Rate of approximation by new sequence of linear positive
operators, Comput. Math. Appl. 45(12) (2003), 1895-1904.
[5] V. Gupta, M. A. Noor, M. S. Beniwal and M. K. Gupta, On simultaneous
approximation for certain Baskakov Durrmeyer type operators, J. Ineq.
Pure Applied Math. 7 (4) (2006) Art. 125, 15 pp.
[6] J. Sinha, V. K. Singh, Rate of convergence on the mixed summation
integral type operators, Gen. Math. 14 (4) (2006), 29-36.
[7] D. K. Verma, V. Gupta and P. N. Agrawal, Some approximation properties
of Baskakov-Durrmeyer-Stancu operators, Appl. Math. Comput., 218 (11)
(2012), 6549-6556.
[8] X. M. Zeng, On the rate of convergence of the generalized Sz'asz type
operators for functions of bounded variation, J. Math. Anal. Appl., 226
(1998), 309-325.
[9] X. M. Zeng, W. Tao, Rate of convergence of the integral type Lupas
operators, J. Kyungpook Math., 43 (2003), 593-604.
[10] X. M. Zeng, X. Cheng, Pointwise approximation by the modified Sz'asz-
Mirakyan operators, J. Comput Anal. Appl., 9 (4) (2007), 421-430.