An estimate of the rate of convergence of a Bézier variant of the Baskakov-Kantorovich operators for bounded variation functions

• Autorzy: Abel U. , Gupta V.
• Języki publikacji: EN

Abstrakty

EN

In the present paper we introduce a Bézier variant of the Baskakov-Kantorovich operators and study the rate of convergence for functions of bounded variation. Furthermore, we present the complete asymptotic expansion for the Baskakov-Kantorovich operators.

Słowa kluczowe

EN

approximation by positive operators; rate of convergence; functions of bounded; total variation

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2003
• Tom: Vol. 36, nr 1
• Strony: 123--136
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Abel U.

• Fachbereich MND, Fachhochschule Giessen-Friedberg, University of Applied Sciences, Wilhelm-Leuschner-Straβe 13, 61169 Friedberg, Germany

autor

Gupta V.

• School of Applied Sciences, Netaji Subhas Institute of Technology, Azad Hind Fauj Marg, Sector-3, Dwarka, New Delhi-110045, India

Bibliografia

• [1] U. Abel, The complete asymptotic expansion for Meyer-König and Zeller operators, J. Math. Anal. Appi. 208 (1997), 109-119.
• [2] G. Aniol, On the rate of pointwise convergence of the Kantorovich-type operators, Fase. Math. 29 (1999), 5-15.
• [3] Z. Ditzian and V. Totik, Moduli of Smoothness, Springer, New York, 1987.
• [4] C. Jordan, Calculus of Finite Differences, Chelsea, New York, 1965.
• [5] P. C. Sikkema, On some linear positive operators, Indag. Math. 32 (1970), 327-337.
• [6] P. C. Sikkema, On the asymptotic approximation with operators of Meyer-König and Zeller, Indag. Math. 32 (1970), 428-440.
• [7] X. M. Zeng, On the rate of convergence of the generalized Szasz type operators for functions of bounded variation, J. Math. Anal. Appl. 226 (1998), 309-325.
• [8] 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.
• [9] X. M. Zeng and W. Chen, On the rate of convergence of the generalized Durrmeyer type operators for functions of bounded variation, J. Approx. Theory 102 (2000), 1-12.
• [10] X. M. Zeng and V. Gupta, Rate of convergence of Baskakov-Bézier type operators for locally bounded functions, Comput. Math. Appl. 44 (2002), 1445-1453.