Rate of convergence of a new type Kantorovich variant of Bleimann-Butzer-Hahn operators. (English) Zbl 1185.41017
Summary: A new type Kantorovich variant of Bleimann-Butzer-Hahn operator \(J_{n}\) is introduced. Furthermore, the approximation properties of the operators \(J_{n}\) are studied. An estimate on the rate of convergence of the operators \(J_{n}\) for functions of bounded variation is obtained.
MSC:
| 41A35 | Approximation by operators (in particular, by integral operators) |
References:
| [1] | Bleimann G, Butzer PL, Hahn L: A Bernstein-type operator approximating continuous functions on the semi-axis.Indagationes Mathematicae 1980,83(3):255-262. 10.1016/1385-7258(80)90027-X · Zbl 0437.41021 · doi:10.1016/1385-7258(80)90027-X |
| [2] | Abel U, Ivan M: A Kantorovich variant of the Bleimann, Butzer and Hahn operators.Rendiconti del Circolo Matematico di Palermo. Serie II. Supplemento 2002, 68: 205-218. · Zbl 1012.41016 |
| [3] | Bojanić R, Vuilleumier M: On the rate of convergence of Fourier-Legendre series of functions of bounded variation.Journal of Approximation Theory 1981,31(1):67-79. 10.1016/0021-9045(81)90031-9 · Zbl 0494.42003 · doi:10.1016/0021-9045(81)90031-9 |
| [4] | Chêng F: On the rate of convergence of Bernstein polynomials of functions of bounded variation.Journal of Approximation Theory 1983,39(3):259-274. 10.1016/0021-9045(83)90098-9 · Zbl 0533.41020 · doi:10.1016/0021-9045(83)90098-9 |
| [5] | Guo SS, Khan MK: On the rate of convergence of some operators on functions of bounded variation.Journal of Approximation Theory 1989,58(1):90-101. 10.1016/0021-9045(89)90011-7 · Zbl 0683.41030 · doi:10.1016/0021-9045(89)90011-7 |
| [6] | Zeng X-M, Piriou A: On the rate of convergence of two Bernstein-Bézier type operators for bounded variation functions.Journal of Approximation Theory 1998,95(3):369-387. 10.1006/jath.1997.3227 · Zbl 0918.41016 · doi:10.1006/jath.1997.3227 |
| [7] | Gupta V, Abel U, Ivan M: Rate of convergence of beta operators of second kind for functions with derivatives of bounded variation.International Journal of Mathematics and Mathematical Sciences 2005,2005(23):3827-3833. 10.1155/IJMMS.2005.3827 · Zbl 1093.41011 · doi:10.1155/IJMMS.2005.3827 |
| [8] | Feller W: An Introduction to Probability Theory and Its Applications. Volume 2. 2nd edition. John Wiley & Sons, New York, NY, USA; 1971:xxiv+669. · Zbl 0219.60003 |
| [9] | Zeng X-M: Bounds for Bernstein basis functions and Meyer-König and Zeller basis functions.Journal of Mathematical Analysis and Applications 1998,219(2):364-376. 10.1006/jmaa.1997.5819 · Zbl 0909.41015 · doi:10.1006/jmaa.1997.5819 |
| [10] | Zeng X-M, Zhao J-N: Exact bounds for some basis functions of approximation operators.Journal of Inequalities and Applications 2001,6(5):563-575. 10.1155/S1025583401000340 · Zbl 0991.41016 · doi:10.1155/S1025583401000340 |
| [11] | Srivastava HM, Gupta V: Rate of convergence for the Bézier variant of the Bleimann-Butzer-Hahn operators.Applied Mathematics Letters 2005,18(8):849-857. 10.1016/j.aml.2004.08.014 · Zbl 1084.41010 · doi:10.1016/j.aml.2004.08.014 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
