A class of continuous functions and their degree of approximation

1977 ◽  
Vol 30 (3-4) ◽  
pp. 227-231 ◽  
Author(s):  
P. D. Kathal ◽  
A. S. B. Holland ◽  
B. N. Sahney
Keyword(s):  
Degree Of Approximation ◽  
Continuous Functions

scholarly journals HOLDER CONTINUOUS FUNCTIONS AND THEIR ABEL AND LOGARITHMIC MEANS

1999 ◽  
Vol 30 (3) ◽  
pp. 167-173
Author(s):  
SUSHIL SHARMA ◽  
S. K. VARMA
Keyword(s):  
Degree Of Approximation ◽  
Continuous Functions ◽  
Infinite Matrix ◽  
Hölder Continuous ◽  
Logarithmic Means ◽  
Hölder Continuous Functions

Mahapatra and Chandra [8] have obtained the degree of approximation for $f \in H_\alpha(0\le \beta<\alpha\le 1)$ using infinite matrix $A = (a_{nk})$. Mahapatra and Chandra [7] used Euler, Boral and Taylor means. In the present paper we have obtained the analogous results using Abel ($A_\lambda$) and Logarithmic ($L$)-means.

scholarly journals Summation-Integral Type Operators Based on Lupas-Jain Functions

2021 ◽  
Vol 45 (02) ◽  
pp. 309-322
Author(s):  
NESIBE MANAV ◽  
NURHAYAT ISPIR
Keyword(s):  
Modulus Of Continuity ◽  
Local Approximation ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Integral Type ◽  
Base Functions

We introduce a genuine summation-integral type operators based on Lupaş-Jain type base functions related to the unbounded sequences. We investigated their degree of approximation in terms of modulus of continuity and ????-functional for the functions from bounded and continuous functions space. Furthermore, we give some theorems for the local approximation properties of functions belonging to Lipschitz class. Also, we give Voronovskaja theorem for these operators.

scholarly journals On the degree of approximation of continuous functions by a specific transform of partial sums of their Fourier series

2021 ◽  
Vol 25 (1) ◽  
pp. 5-19
Author(s):  
Xhevat Krasniqi
Keyword(s):  
Fourier Series ◽  
Continuous Function ◽  
Bounded Variation ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Auxiliary Function ◽  
Partial Sums ◽  
The Mean ◽  
Approximation Of Continuous Functions ◽  
Positive Integers

Using the Mean Rest Bounded Variation Sequences or the Mean Head Bounded Variation Sequences, we have proved four theorems pertaining to the degree of approximation in sup-norm of a continuous function f by general means τλn;A(f) of partial sums of its Fourier series. The degree of approximation is expressed via an auxiliary function H(t) ≥ 0 and via entries of a matrix whose indices form a strictly increasing sequence of positive integers λ := {λ(n)}∞n=1.

Degree of Approximation by Rational Functions with Prescribed Numerator Degree

1994 ◽  
Vol 46 (3) ◽  
pp. 619-633 ◽  
Author(s):  
D. Leviatan ◽  
D. S. Lubinsky
Keyword(s):  
Rational Function ◽  
Modulus Of Continuity ◽  
Special Functions ◽  
Type Theorem ◽  
Rational Functions ◽  
Degree Of Approximation ◽  
Continuous Functions ◽  
Jackson Type ◽  
Jackson Type Theorem ◽  
Approximation By Rational Functions

AbstractWe prove a Jackson type theorem for rational functions with prescribed numerator degree: For continuous functions f: [—1,1] —> ℝ with ℓ sign changes in (—1,1), there exists a real rational function Rℓ,n(x) with numerator degree ℓ and denominator degree at most n, that changes sign exactly where f does, and such thatHere C is independent of f, n and ℓ, and ωφ is the Ditzian-Totik modulus of continuity. For special functions such as f(x) = sign(x)|x|α we consider improvements of the Jackson rate.

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