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.

scholarly journals Trigonometric approximation of functions $f(x,y)$ of generalized Lipschitz class by double Hausdorff matrix summability method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Abhishek Mishra ◽  
Vishnu Narayan Mishra ◽  
M. Mursaleen
Keyword(s):  
Double Fourier Series ◽  
Degree Of Approximation ◽  
Trigonometric Approximation ◽  
Lipschitz Class ◽  
Gamma Delta ◽  
Approximation Of Functions ◽  
Matrix Summability ◽  
Alpha Beta ◽  
Generalized Lipschitz Class ◽  
Hausdorff Matrix

AbstractIn this paper, we establish a new estimate for the degree of approximation of functions $f(x,y)$ f ( x , y ) belonging to the generalized Lipschitz class $Lip ((\xi _{1}, \xi _{2} );r )$ L i p ( ( ξ 1 , ξ 2 ) ; r ) , $r \geq 1$ r ≥ 1 , by double Hausdorff matrix summability means of double Fourier series. We also deduce the degree of approximation of functions from $Lip ((\alpha ,\beta );r )$ L i p ( ( α , β ) ; r ) and $Lip(\alpha ,\beta )$ L i p ( α , β ) in the form of corollary. We establish some auxiliary results on trigonometric approximation for almost Euler means and $(C, \gamma , \delta )$ ( C , γ , δ ) means.

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.

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