Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
In recent papers the authors studied global smoothness preservation by certain univariate and multivariate linear operators over compact domains. Here the domain is ℝ. A very general positive linear integral type operator is introduced through a convolution-like iteration of another general positive linear operator with a scaling type function. For it sufficient conditions are given for shift invariance, preservation of global smoothness, convergence to the unit with rates, shape preserving and preservation of continuous probabilistic functions. Finally, four examples of very general specialized operators are presented fulfilling all the above properties; in particular, the inequalities for global smoothness preservation are proven to be sharp.
Kategorie tematyczne
- 41A55: Approximate quadratures
- 26A18: Iteration
- 26A15: Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.)
- 41A36: Approximation by positive operators
- 41A99: None of the above, but in this section
- 60E05: Distributions: general theory
- 41A35: Approximation by operators (in particular, by integral operators)
- 41A17: Inequalities in approximation (Bernstein, Jackson, Nikol\cprime ski{\u\i}-type inequalities)
- 41A25: Rate of convergence, degree of approximation
Czasopismo
Rocznik
Tom
Numer
Strony
225-243
Opis fizyczny
Daty
wydano
1995
otrzymano
1993-04-20
poprawiono
1994-10-15
Twórcy
autor
- Department of Mathematics, University of Duisburg, D-47048 Duisburg, Germany
autor
- Department of Mathematical Sciences, The University of Memphis, Memphis, Tennessee 38152, U.S.A.
Bibliografia
- [1] G. Anastassiou, C. Cottin and H. Gonska, Global smoothness of approximating functions, Analysis 11 (1991), 43-57.
- [2] G. Anastassiou, C. Cottin and H. Gonska, Global smoothness preservation by multivariate approximation operators, in: Israel Mathematical Conference Proc. 4, Weizmann Science Press, 1991, 31-44.
- [3] G. Anastassiou and X. M. Yu, Monotone and probabilistic wavelet approximation, Stochastic Anal. Appl. 10 (1992), 251-264.
- [4] G. Anastassiou and X. M. Yu, Convex and coconvex-probabilistic wavelet approximation, Stochastic Anal. Appl., 507-521.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
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