On the integral modulus of continuity of Fourier series

1989 ◽  
Vol 99 (3) ◽  
pp. 249-253 ◽  
Author(s):  
Babu Ram ◽  
Suresh Kumari
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Integral Modulus

scholarly journals On the Integral Modulus of Continuity of Fourier Series

1988 ◽  
Vol 44 (2) ◽  
pp. 151-158
Author(s):  
Babu Ram ◽  
Suresh Kumari
Keyword(s):  
Fourier Series ◽  
Trigonometric Series ◽  
Modulus Of Continuity ◽  
Wide Class ◽  
Integral Modulus

AbstractFor a wide class of sine trigonometric series we obtain an estimate for the integral modulus of continuity.

scholarly journals On trigonometric approximation of functions in the Lq norm

2018 ◽  
Vol 51 (1) ◽  
pp. 17-26 ◽  
Author(s):  
Ram N. Mohapatra ◽  
Bogdan Szal
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Infinite Matrix ◽  
Approximation Of Functions ◽  
Integral Modulus

Abstract In this paper we obtain a degree of approximation of functions in Lq by operators associated with their Fourier series using integral modulus of continuity. These results generalize many known results and are proved under less stringent conditions on the infinite matrix.

Uniform and 𝐿-Convergence of Logarithmic Means of Double Walsh–Fourier Series

2005 ◽  
Vol 12 (1) ◽  
pp. 75-88
Author(s):  
György Gát ◽  
Ushangi Goginava
Keyword(s):  
Fourier Series ◽  
Function Space ◽  
Modulus Of Continuity ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Two Dimensional ◽  
Logarithmic Means ◽  
Convergence And Divergence ◽  
Necessary And Sufficient ◽  
Series Of Functions

Abstract We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh–Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.

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