On the orders of the best approximations of integrals of functions by integrals of rank σ

2007 ◽  
Vol 10 (4) ◽  
pp. 0-0
Author(s):  
A. I. Stepanets ◽  
A. L. Shidlich
Keyword(s):  
Best Approximations

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.

Best approximations and fixed points of nonexpansive maps in hilbert spaces sehie park

1997 ◽  
Vol 18 (5-6) ◽  
pp. 447-454 ◽  
Author(s):  
Sehie Park ◽  
Sehie Park ◽  
S. p. Singh ◽  
B. Watson ◽  
T. E. Williamson
Keyword(s):  
Fixed Points ◽  
Hilbert Spaces ◽  
Best Approximations ◽  
Nonexpansive Maps

Im-Quasi Upward Sets, with Their Best Approximations

2010 ◽  
Vol 31 (11) ◽  
pp. 1261-1271
Author(s):  
M. Iranmanesh ◽  
F. Solimany
Keyword(s):  
Best Approximations

scholarly journals CONTINUED FRACTIONS, INTERMEDIATE FRACTIONS AND THEIR RELATION TO THE BEST APPROXIMATIONS

2020 ◽  
Vol 20 (3) ◽  
pp. 545-560
Author(s):  
LUKA MILINKOVIC ◽  
BRANKO MALESEVIC ◽  
BOJAN BANJAC
Keyword(s):  
Continued Fractions ◽  
Continued Fraction ◽  
Rational Approximations ◽  
Best Approximations ◽  
Current State ◽  
The Subject ◽  
State Of Art

The subject of this paper is the current state of art in theory of continued fractions, intermediate fractions and their relation to the best rational approximations of the first and second kind. The paper provides an overview of the some well known and even some new properties of continued fractions, and the various terms associated with them. In addition to intermediate fractions, paper considers the fine intermediate fractions and gave some statements to position these fractions in the continued fraction representation of numbers.

Estimates of Functions with Transformed Double Fourier Series

2021 ◽  
Vol 58 (1) ◽  
pp. 32-83
Author(s):  
Boris V. Simonov
Keyword(s):  
Fourier Series ◽  
Double Fourier Series ◽  
Moduli Of Smoothness ◽  
Best Approximations

The paper provides a detailed study of inequalities of complete moduli of smoothness of functions with transformed Fourier series by moduli of smoothness of initial functions. Upper and lower estimates of the norms and best approximations of the functions with transformed Fourier series by the best approximations of initial functions are also obtained.

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