scholarly journals Direct and Inverse Approximation Theorems for Baskakov Operators with the Jacobi-Type Weight

2011 ◽  
Vol 2011 ◽  
pp. 1-13
Author(s):  
Guo Feng
Keyword(s):  
Baskakov Operators ◽  
Approximation Theorems ◽  
Inverse Approximation

We introduce a new norm and a newK-functionalKφλ(f;t)w,λ. Using thisK-functional, direct and inverse approximation theorems for the Baskakov operators with the Jacobi-type weight are obtained in this paper.

scholarly journals Direct and inverse approximation theorems of functions in the Orlicz type spaces 𝓢M

2019 ◽  
Vol 69 (6) ◽  
pp. 1367-1380 ◽  
Author(s):  
Stanislav Chaichenko ◽  
Andrii Shidlich ◽  
Fahreddin Abdullayev
Keyword(s):  
Fractional Order ◽  
Moduli Of Smoothness ◽  
Best Approximations ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Type Spaces

Abstract In the Orlicz type spaces 𝓢M, we prove direct and inverse approximation theorems in terms of the best approximations of functions and moduli of smoothness of fractional order. We also show the equivalence between moduli of smoothness and Peetre K-functionals in the spaces 𝓢M.

scholarly journals Direct and inverse approximation theorems in the weighted Orlicz-type spaceswith a variable exponent

2020 ◽  
Vol 44 (1) ◽  
pp. 284-299
Author(s):  
Fahreddin ABDULLAYEV ◽  
Stanislav CHAICHENKO ◽  
Meerim IMASH KYZY ◽  
Andrii SHIDLICH
Keyword(s):  
Variable Exponent ◽  
Approximation Theorems ◽  
Inverse Approximation

DIRECT AND INVERSE APPROXIMATION THEOREMS FOR THE p-VERSION OF THE FINITE ELEMENT METHOD IN THE FRAMEWORK OF WEIGHTED BESOV SPACES PART II: OPTIMAL RATE OF CONVERGENCE OF THE p-VERSION FINITE ELEMENT SOLUTIONS

2002 ◽  
Vol 12 (05) ◽  
pp. 689-719 ◽  
Author(s):  
IVO BABUŠKA ◽  
BENQI GUO
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Rate Of Convergence ◽  
Besov Spaces ◽  
The Finite Element Method ◽  
Optimal Rate Of Convergence ◽  
Approximation Theorems ◽  
Inverse Approximation ◽  
Weighted Besov Spaces ◽  
Element Method

This is the second of a series devoted to the direct and inverse approximation theorems of the p-version of the finite element method in the framework of the weighted Besov spaces. In this paper, we combine the approximability of singular solutions in the Jacobi-weighted Besov spaces, which were analyzed in the previous paper,4 with the technique of partition of unity in order to prove the optimal rate of convergence of the p-version of the finite element method for elliptic boundary value problems on polygonal domains.

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