On the Approximation Properties of Cesàro Means of Negative Order for the Double Vilenkin–Fourier Series

2020 ◽  
Vol 72 (3) ◽  
pp. 446-463
Author(s):  
T. Tepnadze
Keyword(s):  
Fourier Series ◽  
Cesàro Means ◽  
Approximation Properties ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means

On the approximation properties of Cesàro means of negative order of Vilenkin—Fourier series

2016 ◽  
Vol 53 (4) ◽  
pp. 532-544
Author(s):  
Tsitsino Tepnadze
Keyword(s):  
Fourier Series ◽  
Cesàro Means ◽  
Approximation Properties ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means

In this paper we establish approximation properties of Cesàro (C, −α) means with α ∈ (0, 1) of Vilenkin—Fourier series. This result allows one to obtain a condition which is sufficient for the convergence of the means σn−α(f, x) to f(x) in the Lp-metric.

scholarly journals On the approximation properties of Cesàro means of negative order of double Vilenkin – Fourier series

2020 ◽  
Vol 72 (3) ◽  
pp. 391-406
Author(s):  
T. Tepnadze
Keyword(s):  
Fourier Series ◽  
Cesàro Means ◽  
Approximation Properties ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means

UDC 517.5 We establish approximation properties of Ces\`{a}ro means with α , β ϵ ( 0,1 ) of Vilenkin\,--\,Fourier series. This result allows one to obtain a condition which is sufficient for the convergence of the means σ n , m - α , - β ( x , y , f ) to f ( x , y ) in the L p -metric.

scholarly journals On the convergence of Cesàro means of negative order of Vilenkin-Fourier series

2019 ◽  
Vol 56 (1) ◽  
pp. 22-44
Author(s):  
Gvantsa Shavardenidze
Keyword(s):  
Fourier Series ◽  
Continuous Function ◽  
Uniform Convergence ◽  
Sufficient Conditions ◽  
Sufficient Condition ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means

Abstract In 1971 Onnewer and Waterman establish a sufficient condition which guarantees uniform convergence of Vilenkin-Fourier series of continuous function. In this paper we consider different classes of functions of generalized bounded oscillation and in the terms of these classes there are established sufficient conditions for uniform convergence of Cesàro means of negative order.

Uniform summability of double Walsh-Fourier series of functions of bounded partial Λ-variation

2014 ◽  
Vol 64 (6) ◽  
Author(s):  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Necessary Conditions ◽  
Partial Sums ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Uniformly Convergence ◽  
Negative Order ◽  
Cesáro Means ◽  
Sufficient And Necessary Conditions ◽  
Series Of Functions

AbstractThe sufficient and necessary conditions on the sequence Λ = {λn} are found for the uniformly convergence of Cesàro means of negative order of cubic partial sums of double Walsh-Fourier series of functions of bounded partial Λ-variation.

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