Taiwanese Journal of Mathematics


Mehmet Ali O¨ zarslan and Oktay Duman

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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.

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Taiwanese J. Math., Volume 12, Number 5 (2008), 1147-1163.

First available in Project Euclid: 20 July 2017

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Mathematical Reviews number (MathSciNet)

Primary: 41A25: Rate of convergence, degree of approximation 41A36: Approximation by positive operators

Poisson integrals orthogonal polynomials positive linear operators $L^{p}$ space modulus of continuity Lipschitz class functionals the Voronovskaya theorem $T-$statistical convergence


O¨ zarslan, Mehmet Ali; Duman, Oktay. APPROXIMATION PROPERTIES OF POISSON INTEGRALS FOR ORTHOGONAL EXPANSIONS. Taiwanese J. Math. 12 (2008), no. 5, 1147--1163. doi:10.11650/twjm/1500574254. https://projecteuclid.org/euclid.twjm/1500574254

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