On the Baskakov-Durrmeyer type operators

• Autorzy: Malejki, R. , Wachnicki, E.
• Języki publikacji: EN

Abstrakty

EN

In this paper we will study some approximate properties of Baskakov-Durrmeyer type operators M^α,a_n. We determine the rate of convergence and prove the Voronovskaya type theorem for those operators.

Słowa kluczowe

EN

Baskakov-Durrmeyer type operators; approximation linear positive operators; rate of convergence; Voronovskaya type theorem

• Czasopismo: Commentationes Mathematicae
• Rocznik: 2014
• Tom: Vol 54, No. 1
• Strony: 39--49
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Malejki, R.

• Institute of Mathematics, Pedagogical University ul. Podchorążych 2, 30-084 Kraków, Poland,

autor

Wachnicki, E.

• Institute of Mathematics, Pedagogical University ul. Podchorążych 2, 30-084 Kraków, Poland,

Bibliografia

• [1] Z. Ditzian, Direct estimate for Bernstein polynomials, J. Approx. Theory 79 (1994), 165–166.
• [2] A. Eren¸cin, Durrmeyer type modification of generalized Baskakov operators, Appl. Math. Comput. 218,(2011), 4384–4390.
• [3] G. Krech, A note on the paper ”Voronovskaya type asymptotic approximation by modified Gamma operators”, Appl. Math. Comput. 219 (2013), 5787–5791.
• [4] G. Krech, On some approximation theorems for the Poisson integral for Hermite expansions, Anal. Math. 40 (2014), 133–145.
• [5] G. Krech, E. Wachnicki, Direct estimate for some operators of Durrmeyer type in exponential weighted space, Demonstratio Math. 47(2) (2014), 336–349.
• [6] S. M. Mazhar, V. Totik, Approximation by modified Sz´asz operators, Acta Sci. Math. 49, (1985), 257–269.
• [7] V. Mihe¸san, Uniform approximation with positive linear operators generalized Baskakov method, Automat. Comput. Appl. Math. 7 (1) (1998), 34–37.
• [8] A. F. Timan, Theory of Approximation of Function of a Real Variable, Moscow 1960 [in Russian].
• [9] V. Totik, Uniform approximation by Sz´asz-Mirakjan type operators, Acta Math. Hungar. 41(3-4) (1983), 291–307.
• [10] A. Wafi, S. Khatoon, On the order of approximation of functions by generalized Baskakov operators, Indian J. Pure Appl. Math. 35 (3) (2004), 347–358.
• [11] A. Wafi, S. Khatoon, Direct and inverse theorems for generalized Baskakov operators in polynomial weight space, An. Stiint. Univ. Al. I. Cuza Iasi. Mat. (N.S) 50 (1) (2004), 159–173.

Identyfikatory

DOI

10.14708/cm.v54i1.760