On the Kantorovich variant of generalized Bernstein type rational functions

• Autorzy: Gupta V. , Ispir N.
• Języki publikacji: EN

Abstrakty

EN

In the present paper we define Kantorovich variant of generalized Bernstein type rational functions. We establish the order of approximation for continuous functions in different normed spaces and also estimate the rate of convergence for functions of bounded variation.

Słowa kluczowe

EN

bounded variation; total variation; Balazs operators; approximations; Bernstein type rational functions

PL

wariacje ograniczone; wariacje zupełne; operatory Balazsa; aproksymacje; funkcje wymierne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 117--130
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Gupta V.

autor

Ispir N.

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

Bibliografia

• [1] O. Agratini, An approximation process of Kantorovich type, Math. Notes, Miskolc 2 (1) (2001), 3-10.
• [2] K. Balazs, Approximation by Bernstein type rational functions, Acta Math. Hungar. 26 (1-2) (1975), 123-134.
• [3] C. Balazs and J. Szabados, Approximation by Bernstein type rational functions II, Acta Math. Hungar. 40 (3-4) (1982), 331-337.
• [4] A.D. Gadzhiev and N. ˙Ispi r, On a sequence of linear positive operators in weighted spaces, Proc. Inst. Math. Mech. Vol. XI, (1999), 45-56.
• [5] V. Gupta and U. Abel, On the rate of convergence of Bezier variant of Szasz-Durrmeyer operators, Anal. Theory and Appl. 19:1 (2003), 81-88.
• [6] N. Ispir and Ç . Atakut, Approximation by generalized Balazs type rational functions, Int. J. Comput. Numer. Anal. Appl. Vol.4, No. 3, (2003), 297-316.
• [7] N. Ispir, On modified Baskakov operators on weighted spaces, Turk. J. Math. Vol. 25, No. 3, (2001), 355-365.
• [8] 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.
• [9] X. M. Zeng, Bounds for Bernstein basis functions and Meyer-Konig-Zeller basis functions, J. Math. Anal. Appl. 219 (1998), 364-376.
• [10] X. M. Zeng and A. Piriou, On the rate of convergence of two Bernstein Bezier type operators for functions of bounded variation, J. Approx. Theory 95 (1998), 369-387.