论文信息 - A quantitative asymptotic formula for a general class of discrete operators

A quantitative asymptotic formula for a general class of discrete operators

Here we give some quantitative versions of the Voronovskaja formula for a general class of discrete operators, not necessarily positive. Applications to various generalizations of the Szasz-Mirak'jan operator and a Jackson type sampling operator are given.

Carlo Bardaro | Ilaria Mantellini

[1] Hugo Ribeiro,et al. Notas de Matemática , 1949 .

[2] J. P. King. Positive linear operators which preserve x2 , 2003 .

[3] Francesco Altomare,et al. Korovkin-type approximation theory and its applications , 1994 .

[4] Heiner Gonska,et al. General King-Type Operators , 2009 .

[5] E. M. Semenov,et al. LACK OF INTERPOLATION OF LINEAR OPERATORS IN SPACES OF SMOOTH FUNCTIONS , 1977 .

[6] P. Butzer,et al. Voronovskaya-Type Theorems for Derivatives of the Bernstein-Chlodovsky Polynomials and the Szász-Mirakyan Operator , 2009 .

[7] M. Ali Özarslan,et al. Szász-Mirakjan type operators providing a better error estimation , 2007, Appl. Math. Lett..

[8] Paul L. Butzer,et al. Linear Prediction by Samples from the Past , 1993 .

[9] Octavian Agratini. Linear operators that preserve some test functions , 2006, Int. J. Math. Math. Sci..

[10] G. Lorentz. Approximation of Functions , 1966 .

[11] O. Szâsz. Generalization of S. Bernstein's Polynomials to the Infinite Interval , 1950 .

[12] L. Maligranda. The K-functional for symmetric spaces , 1984 .

[13] I. S. Gradshteyn,et al. Table of Integrals, Series, and Products , 1976 .

[14] George A. Anastassiou,et al. Approximation theory - moduli of continuity and global smoothness preservation , 1999 .

[15] Paul L. Butzer,et al. Fourier analysis and approximation , 1971 .