scholarly journals Some estimates of approximation of functions by Hermitian splines

1987 ◽  
pp. 23
Author(s):  
O.V. Davydov
Keyword(s):  
Modulus Of Continuity ◽  
Duality Theorem ◽  
Localization Theorem ◽  
Approximation Of Functions ◽  
Uniform Partition ◽  
Integral Modulus ◽  
Differentiable Functions

We find exact values of approximation by Hermitian splines on the classes of differentiable functions in three new cases, which add to the researches of V.L. Velikin. We obtain the estimate of deviation, which uses the values of integral modulus of continuity. Besides, we generalize the duality theorem of A.A. Ligun and prove the localization theorem that allows to determine the optimality of the uniform partition in the most general case.

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.

On the integral modulus of continuity of fourier series

1975 ◽  
Vol 28 (1) ◽  
pp. 78-85 ◽  
Author(s):  
Babu Ram
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Integral Modulus

scholarly journals On approximation by trigonometrical polynomials in $L_2$ space

2016 ◽  
Vol 24 ◽  
pp. 89
Author(s):  
O.V. Polyakov
Keyword(s):  
Modulus Of Continuity ◽  
Best Approximation ◽  
Generalized Modulus Of Continuity ◽  
Jackson Type ◽  
The Best Approximation ◽  
Differentiable Functions

We obtain certain inequalities of Jackson type, connecting the value of the best approximation of periodic differentiable functions and the generalized modulus of continuity of the highest derivative.

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.

Approximation of functions by some exponential operators of max-product type

2019 ◽  
Vol 56 (1) ◽  
pp. 94-102
Author(s):  
Adrian Holhoş
Keyword(s):  
Modulus Of Continuity ◽  
Uniform Approximation ◽  
Product Type ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Rate Of Approximation

Abstract In this paper we study the uniform approximation of functions by a generalization of the Picard and Gauss-Weierstrass operators of max-product type in exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. We extend and improve previous results.

On the integral modulus of continuity of Fourier series

1972 ◽  
Vol 58 (1) ◽  
pp. 337-343
Author(s):  
Babu Ram
Keyword(s):  
Fourier Series ◽  
Modulus Of Continuity ◽  
Integral Modulus
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