scholarly journals Approximation by rational functions on doubly connected domains in weighted generalized grand Smirnov classes

2021 ◽  
Vol 73 (7) ◽  
pp. 964-978
Author(s):  
A. Testici
Keyword(s):  
Connected Domain ◽  
Analytic Functions ◽  
Rational Functions ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Doubly Connected Domain ◽  
Smirnov Classes ◽  
Approximation By Rational Functions

UDC 517.5 Let be a doubly connected domain bounded by two rectifiable Carleson curves. In this work, we use the higher modulus of smoothness in order to investigate the approximation properties of -Faber–Laurent rational functions in the subclass of weighted generalized grand Smirnov classes of analytic functions.

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.

scholarly journals Gamma Generalization Operators Involving Analytic Functions

Mathematics ◽  
2021 ◽  
Vol 9 (13) ◽  
pp. 1547
Author(s):  
Qing-Bo Cai ◽  
Bayram Çekim ◽  
Gürhan İçöz
Keyword(s):  
Rate Of Convergence ◽  
Gamma Function ◽  
Analytic Functions ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
First Order

In the present paper, we give an operator with the help of a generalization of Boas–Buck type polynomials by means of Gamma function. We have approximation properties and moments. The rate of convergence is given by the Ditzian–Totik first order modulus of smoothness and the K-functional. Furthermore, we obtain the point-wise estimations for this operator.

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