Uniform Approximation of Functions of Two Variables

2017 ◽  
Vol 53 (3) ◽  
pp. 426-431 ◽  
Author(s):  
P. S. Malachivskyy ◽  
Ya. N. Matviychuk ◽  
Ya. V. Pizyur ◽  
R. P. Malachivskyi
Keyword(s):  
Uniform Approximation ◽  
Approximation Of Functions ◽  
Functions Of Two Variables

Approximation of functions by some exponential operators of max-product type

2019 ◽  
Vol 56 (1) ◽  
pp. 94-102
Author(s):  
Adrian Holhoş
Keyword(s):  
Modulus Of Continuity ◽  
Uniform Approximation ◽  
Product Type ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Rate Of Approximation

Abstract In this paper we study the uniform approximation of functions by a generalization of the Picard and Gauss-Weierstrass operators of max-product type in exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity. We extend and improve previous results.

scholarly journals A note on uniform approximation of functions having a double pole

2014 ◽  
Vol 17 (1) ◽  
pp. 233-244
Author(s):  
Ionela Moale ◽  
Veronika Pillwein
Keyword(s):  
Symbolic Computation ◽  
Uniform Approximation ◽  
Classical Problem ◽  
Type Equation ◽  
Elliptic Functions ◽  
Double Pole ◽  
Approximation Of Functions ◽  
Best Uniform Approximation ◽  
Approximation By Polynomials ◽  
Low Degrees

AbstractWe consider the classical problem of finding the best uniform approximation by polynomials of$1/(x-a)^2,$where$a>1$is given, on the interval$[-\! 1,1]$. First, using symbolic computation tools we derive the explicit expressions of the polynomials of best approximation of low degrees and then give a parametric solution of the problem in terms of elliptic functions. Symbolic computation is invoked then once more to derive a recurrence relation for the coefficients of the polynomials of best uniform approximation based on a Pell-type equation satisfied by the solutions.

scholarly journals Approximation of functions and their conjugates in Lp and uniform metric by Euler means

2018 ◽  
Vol 51 (1) ◽  
pp. 141-150
Author(s):  
Sergey S. Volosivets ◽  
Anna A. Tyuleneva
Keyword(s):  
Uniform Approximation ◽  
Conjugate Functions ◽  
Periodic Functions ◽  
Best Approximations ◽  
Approximation Of Functions

Abstract For 2π-periodic functions from Lp (where 1 < p < ∞) we prove an estimate of approximation by Euler means in Lp metric generalizing a result of L. Rempuska and K. Tomczak. Furthermore, we show that this estimate is sharp in a certain sense. We study the uniform approximation of functions by Euler means in terms of their best approximations in p-variational metric and also prove the sharpness of this estimate under some conditions. Similar problems are treated for conjugate functions.

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