Direct and Inverse Theorems of the Theory of Approximation. Equivalent Norms

1975 ◽  
pp. 183-230
Author(s):  
S. M. Nikol’skii
Keyword(s):  
Equivalent Norms ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems

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.

Approximation in weighted generalized grand smirnov classes

2017 ◽  
Vol 54 (4) ◽  
pp. 471-488 ◽  
Author(s):  
Daniyal M. Israfilov ◽  
Ahmet Testici
Keyword(s):  
Complex Plane ◽  
Approximation Theory ◽  
Connected Domain ◽  
Modulus Of Smoothness ◽  
Algebraic Polynomials ◽  
Lipschitz Classes ◽  
Carleson Curve ◽  
Smirnov Classes ◽  
Direct And Inverse Theorems ◽  
Inverse Theorems

Let G be a finite simple connected domain in the complex plane C, bounded by a Carleson curve Γ := ∂G. In this work the direct and inverse theorems of approximation theory by the algebraic polynomials in the weighted generalized grand Smirnov classes εp),θ(G,ω) and , 1 < p < ∞, in the term of the rth, r = 1, 2,..., mean modulus of smoothness are proved. As a corollary the constructive characterizations of the weighted generalized grand Lipschitz classes are obtained.

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