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 Approximation of functions by Favard-Szász-Mirakyan operators of max-product type in weighted spaces

Filomat ◽  
2018 ◽  
Vol 32 (7) ◽  
pp. 2567-2576
Author(s):  
Adrian Holhoş
Keyword(s):  
Modulus Of Continuity ◽  
Uniform Approximation ◽  
Product Type ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Rate Of Approximation

In this paper we study the uniform approximation of functions by Favard-Sz?sz-Mirakyan operators of max-product type in some exponential weighted spaces. We estimate the rate of approximation in terms of a suitable modulus of continuity.

Uniform approximation of functions by Bernstein-Stancu operators

2015 ◽  
Vol 31 (2) ◽  
pp. 205-212
Author(s):  
ADRIAN HOLHOS ◽  
Keyword(s):  
Uniform Approximation ◽  
Continuous Functions ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Stancu Operators ◽  
Jacobi Weights

For the class of bounded and continuous functions on (0, 1) we give a characterization of the functions which can be uniformly approximated by Bernstein-Stancu operators. We also study the possibility of uniform approximation of unbounded functions by Bernstein-Stancu operators in weighted spaces with Jacobi weights.

Modified Lupaş-Jain operators

2020 ◽  
Vol 70 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Murat Bodur
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Order Of Approximation ◽  
Weighted Modulus Of Continuity ◽  
Quantitative Form ◽  
Voronovskaya Type Theorem ◽  
Weighted Modulus

Abstract The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

scholarly journals Approximation by a composition of Chlodowsky operators and Százs–Durrmeyer operators on weighted spaces

2013 ◽  
Vol 16 ◽  
pp. 388-397 ◽  
Author(s):  
Aydın İzgi
Keyword(s):  
Modulus Of Continuity ◽  
Weighted Spaces ◽  
Order Of Approximation ◽  
Weighted Modulus Of Continuity ◽  
Durrmeyer Operators ◽  
Basic Properties ◽  
Weighted Modulus ◽  
Image Position

AbstractIn this paper we deal with the operators $$\begin{eqnarray*}{Z}_{n} (f; x)= \frac{n}{{b}_{n} } { \mathop{\sum }\nolimits}_{k= 0}^{n} {p}_{n, k} \biggl(\frac{x}{{b}_{n} } \biggr)\int \nolimits \nolimits_{0}^{\infty } {s}_{n, k} \biggl(\frac{t}{{b}_{n} } \biggr)f(t)\hspace{0.167em} dt, \quad 0\leq x\leq {b}_{n}\end{eqnarray*}$$ and study some basic properties of these operators where ${p}_{n, k} (u)=\bigl(\hspace{-4pt}{\scriptsize \begin{array}{ l} \displaystyle n\\ \displaystyle k\end{array} } \hspace{-4pt}\bigr){u}^{k} \mathop{(1- u)}\nolimits ^{n- k} , (0\leq k\leq n), u\in [0, 1] $ and ${s}_{n, k} (u)= {e}^{- nu} \mathop{(nu)}\nolimits ^{k} \hspace{-3pt}/ k!, u\in [0, \infty )$. Also, we establish the order of approximation by using weighted modulus of continuity.

scholarly journals Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

2020 ◽  
Author(s):  
M. Mursaleen ◽  
Md Nasiruzzaman ◽  
Adem Kilicman ◽  
Siti Hasana Sapar
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Second Order ◽  
Maximal Functions ◽  
Weighted Spaces ◽  
Phillips Operators ◽  
Convergence Results

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

Approximation of Functions by Polynomials in C[-L, 1]

1992 ◽  
Vol 44 (5) ◽  
pp. 924-940 ◽  
Author(s):  
Z. Ditzian ◽  
D. Jiang
Keyword(s):  
Pointwise Estimate ◽  
Approximation Of Functions ◽  
Norm Estimates ◽  
Rate Of Approximation ◽  
Converse Result ◽  
Approximation By Polynomials ◽  
Classical Estimate ◽  
Approximating Polynomials ◽  
Derivatives Of

AbstractA pointwise estimate for the rate of approximation by polynomials , For 0 ≤ ƛ ≤ 1, integer r, and δn(x) = n-1 + φ(x), is achieved here. This formula bridges the gap between the classical estimate mentioned in most texts on approximation and obtained by Timan and others (ƛ = 0) and the recently developed estimate by Totik and first author (ƛ = 1 ). Furthermore, a matching converse result and estimates on derivatives of the approximating polynomials and their rate of approximation are derived. These results also cover the range between the classical pointwise results and the modern norm estimates for C[— 1,1].

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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