Isaac Scientific Publishing

Journal of Advances in Applied Mathematics

A Study of Weighted Polynomial Approximations for Orthogonal Polynomial Expansion

Download PDF (642.7 KB) PP. 173 - 195 Pub. Date: July 31, 2017

DOI: 10.22606/jaam.2017.23007


  • Ryozi Sakai*
    Department of Mathematics, Meijo University, Tenpaku-ku, Nagoya 468-8502, Japan


We investigate weighted polynomial approximations. Especially, we will study some facts related to the Fourier-type orthogonal expansion and the de la Vall´ee Poussin means. Then the estimate of the modulus of smoothness is important. To complete the theorems we need the Nikolskii-type inequality, higher order derivatives of approximation polynomials, the function with bounded variation, and others.


Fourier-type orthogonal expansions, De la Vall´ee Poussin means, Modulus of smoothness.


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