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Start Over Subject uniform convergence

1. The sharpness of convergence results for $q$-Bernstein polynomials in the case $q>1$

Creator:
Ostrovska, Sofiya
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
$q$-integers, $q$-binomial coefficients, $q$-Bernstein polynomials, uniform convergence, analytic function, and Cauchy estimates
Language:
English
Description:
Due to the fact that in the case $q>1$ the $q$-Bernstein polynomials are no longer positive linear operators on $C[0,1],$ the study of their convergence properties turns out to be essentially more difficult than that for $q<1.$ In this paper, new saturation theorems related to the convergence of $q$-Bernstein polynomials in the case $q>1$ are proved.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Uniform convergence of double trigonometric series

Creator:
Kórus, Péter
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
sine series, cosine series, double sine series, sine-cosine series, double cosine series, uniform convergence, regular convergence, general monotone sequence, general monotone double sequence, and supremum bounded variation
Language:
English
Description:
It is a classical problem in Fourier analysis to give conditions for a single sine or cosine series to be uniformly convergent. Several authors gave conditions for this problem supposing that the coefficients are monotone, non-negative or more recently, general monotone. There are also results for the regular convergence of double sine series to be uniform in case the coefficients are monotone or general monotone double sequences. In this paper we give new sufficient conditions for the uniformity of the regular convergence of sine-cosine and double cosine series, which are necessary as well in case the coefficients are non-negative. The new results also bring necessary and sufficient conditions for the uniform regular convergence of double trigonometric series in complex form.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public