Using wavelets for Szász-type operators
Keywords:
compactly supported wavelets, Szász type operators, second-order Lipschitz continuity, inverse theorems, K-functionalAbstract
Szász-Mirakjan operators extend the classical Bernstein operators and are useful tools for approximating continuous functions on the infinite interval
These operators have integral variations of Kantorovich and Durrmeyer types in order to approximate
In this paper we introduce a class of Szász type operators by means of Daubechies' compactly supported wavelets. These new operators can be used to characterize the second-order Lipschitz continuity of continuous functions and to approximate
We also provide direct and inverse theorems of these operators for these purposes.
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References
M. Becker, Global approximation theorems for Szász-Mirakjan and Baskakov operators in polynomial weight spaces, Indiana Univ. Math. J. 27(1978), pp. 127-142.
H. Beres and G.G. Lorentz, Inverse theorems for Bernstein polynomials, Indiana Univ. Math. J. 21 (1972), pp. 693-708.
I. Daubechies, Orthonormal bases of compactly supported wavelets, Comm. Pure Appl. Math. 41 (1988), pp. 909-996.
I. Daubechies, Ten Lectures on Wavelets, CBMS-NSF Series in Appl. Math. 61, SIAM Publ., Philadelphia, 1992.
Z. Ditzian and V. Totik, Moduli of Smoothness, Springer Series in Computational Mathematics vol. 9, Springer-Verlag, Berlin/Heidelberg/New York, 1987.,
Zhu-Rui Gou and Ding-Xuan Zhou, Approixmation theorems for modified Szász operators, Acta Sci. Mat. (Sgedeg) 56 (1992), pp. 311-321.
M. Heilmann, Direct and converse results for operators of Baskakov-Durrmeyer type, Approx. Theory Appl. 5 (1989), pp. 105-127.
D. Mach and Ding-Xuan Zhou, Approximation theorems for a class of Bernstein-Durrmeyer operators, preprint, 1993.
S.M. Mazhar and V. Totik, Approximation by modified Szász operators, Acta Sci. Math. (Szeged) 49 (1985), pp. 257-269.
V. Totik, Uniform approximation by Sza'sz-Mirakjan type operators, Acta Math. Hungar. 41 (1983), pp. 291-307.
Mao-Dong Ye and Ding-Xuan Zhou, A class of operators by means of three-diagonal matrices, J. Approx. Theory 78 (1994), pp. 239-259.
Ding-Xuan Zhou, On a paper of Mazhar and Totik, J. Approx. theory. 72 (1993), pp. 290-300.
Ding-Xuan Zhou, Uniform approximation by some Dyrrmeyer operators, Approx. Theory Appl. 6(1990), pp. 87-100.
Ding-Xuan Zhou, On smoothness characterized by Bernstein type operators, J. Approx. theory, to appear.
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