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Title: Approximation properties of Poisson integrals for orthogonal expansions
Authors: Özarslan, Mehmet Ali
Duman, Oktay
Keywords: Poisson integrals
orthogonal polynomials
positive linear operators
L(p) space
modulus of continuity
Lipschitz class functionals
the Voronovskaya theorem
T-statistical convergence
Issue Date: 2008
Publisher: Mathematical Soc Rep China
Abstract: In the present paper we introduce Poisson type integrals for orthogonal expansions. We first give some direct computations for the moments and compute the rates of convergence by means of the modulus of continuity and the Lipschitz functionals; and also we prove that our results are stronger and more general than the results obtained by Toczek and Wachnicki [J. Approx. Theory 116 (2002), 113-125]. We obtain a statistical approximation theorem by using the concept of T-statistical convergence which is a (non-matrix) summability transformation. Furthermore, we give a general Voronovskaya type theorem for these operators. Finally, introducing a higher order generalization of Poisson integrals we discuss their approximation properties.
ISSN: 1027-5487
Appears in Collections:Matematik Bölümü / Department of Mathematics
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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