On the convergence of Cesàro means of negative order of double trigonometric Fourier series of functions of bounded partial generalized variation

2011 ◽  
Vol 77 (3-4) ◽  
pp. 451-471
Author(s):  
Ushangi Goginava ◽  
Artur Sahakian
Keyword(s):  
Fourier Series ◽  
Trigonometric Fourier Series ◽  
Cesàro Means ◽  
Cesaro Means ◽  
Negative Order ◽  
Cesáro Means ◽  
Generalized Variation ◽  
Series Of Functions

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.

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.

On the Approximate Properties of Generalized Cesàro Means of Conjugate Trigonometric Fourier Series

2009 ◽  
Vol 16 (3) ◽  
pp. 413-425
Author(s):  
Teimuraz Akhobadze
Keyword(s):  
Fourier Series ◽  
Continuous Functions ◽  
Trigonometric Fourier Series ◽  
Cesàro Means ◽  
Space Of Continuous Functions ◽  
Cesaro Means ◽  
Cesáro Means ◽  
Generalized Cesàro Means

Abstract The behavior of generalized Cesàro (𝐶, α 𝑛)-means (α 𝑛 ∈ (–1, 0), 𝑛 = 1, 2, . . .) of conjugate trigonometric Fourier series of 𝐻𝑤 classes in the space of continuous functions is studied.

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