An asymptotic formula for a class of approximation processes of King’s type

Abstract


In this paper we present a general class of linear positive operators of discrete type reproducing the third test function of Korovkin theorem. In a certain weighted space it forms an approximation process. A Voronovskaja-type result is established and particular cases are analyzed.

Authors

Octavian Agratini
Department of Mathematics, Babes-Bolyai University, Cluj-Napoca, Romania

Keywords

Approximation process; statistical convergence; Voronovskaja type fromula.

Paper coordinates

O. Agratini, An asymptotic formula for a class of approximation processes of King’s type, Studia Scientiarum Mathematicarum Hungarica, 47 (2010) no. 4, pp. 435-444, https://doi.org/10.1556/sscmath.2009.1142.

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Studia Scientiarum Mathematicarum Hungarica

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[1] Agratini, O., Linear operators that preserve some test functions, Int. J. Math. Math. Sci., Vol. 2006, Article ID 94136, p. 11 (2006). MR 2007e:41025
[2] Becker, M., Global approximation theorems for Szász–Mirakyan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J., 27 (1978), no. 1, 127–142. MR 58#12116
[3] Gadjiev, A. D. and Orhan, C., Some approximation theorems via statistical convergence, Rocky Mountain J. Math., 32 (2002), no. 1, 129–138. MR 2003f:41041
[4] King, J. P., Positive linear operators which preserve x2, Acta Math. Hungar., 99 (2003), no. 3, 203–208. MR 2004e:41027
[5] May, C. P., Saturation and inverse theorems for combinations of a class of exponential-type operators, Canad. J. Math., 28 (1976), no. 6, 1224–1250. MR 55#8640

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