Direct and inverse theorems for best approximation by Λ-Splines

1976 ◽  
pp. 116-131 ◽  
Author(s):  
H. Johnen ◽  
K. Scherer
Keyword(s):  
Best Approximation ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems

scholarly journals Approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces

2021 ◽  
Vol 13 (3) ◽  
pp. 750-763
Author(s):  
Z. Cakir ◽  
C. Aykol ◽  
V.S. Guliyev ◽  
A. Serbetci
Keyword(s):  
Best Approximation ◽  
Variable Exponent ◽  
Modulus Of Smoothness ◽  
Morrey Spaces ◽  
Trigonometric Polynomials ◽  
The Best Approximation ◽  
Weighted Morrey Spaces ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems

In this paper we investigate the best approximation by trigonometric polynomials in the variable exponent weighted Morrey spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$, where $w$ is a weight function in the Muckenhoupt $A_{p(\cdot)}(I_{0})$ class. We get a characterization of $K$-functionals in terms of the modulus of smoothness in the spaces ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$. Finally, we prove the direct and inverse theorems of approximation by trigonometric polynomials in the spaces ${\mathcal{\widetilde{M}}}_{p(\cdot),\lambda(\cdot)}(I_{0},w),$ the closure of the set of all trigonometric polynomials in ${\mathcal{M}}_{p(\cdot),\lambda(\cdot)}(I_{0},w)$.

Approximation by trigonometric polynomials in the framework of variable exponent grand Lebesgue spaces

2016 ◽  
Vol 23 (1) ◽  
Author(s):  
Nina Danelia ◽  
Vakhtang Kokilashvili
Keyword(s):  
Lebesgue Space ◽  
Variable Exponent ◽  
Trigonometric Polynomials ◽  
Lebesgue Spaces ◽  
Variable Exponent Lebesgue Space ◽  
Grand Lebesgue Spaces ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems ◽  
Grand Lebesgue Space

AbstractIn this paper we establish direct and inverse theorems on approximation by trigonometric polynomials for the functions of the closure of the variable exponent Lebesgue space in the variable exponent grand Lebesgue space.

scholarly journals Some direct and inverse theorems in approximation of functions

1983 ◽  
Vol 34 (2) ◽  
pp. 143-154 ◽  
Author(s):  
R. N. Mohapatra ◽  
D. C. Russell
Keyword(s):  
Fourier Series ◽  
Linear Operators ◽  
Approximation Of Functions ◽  
Inverse Results ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems ◽  
Degree Of Convergence

AbstractThe paper is concerned with the determination of the degree of convergence of a sequence of linear operators connected with the Fourier series of a function of class Lp (p > 1) to that function and some inverse results in relating the convergence to the classes of functions. In certain cases one can obtain the saturation results too. In all cases Lp norm is used.

Sign in / Sign up

Export Citation Format

Share Document