A note on Baskakov operators based on a function ϑ

2016 ◽  
Vol 25 (1) ◽  
pp. 15-27
Author(s):  
DIDEM AYDIN ARI ◽  
◽  
ALI ARAL ◽  
DANIEL CARDENAS-MORALES ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Modulus Of Continuity ◽  
Shape Preserving ◽  
Baskakov Operators ◽  
Qualitative And Quantitative ◽  
First Order ◽  
Voronovskaya Type Theorem ◽  
Monotonic Convergence ◽  
Weighted Modulus

In this paper, we consider a modification of the classical Baskakov operators based on a function ϑ. Basic qualitative and quantitative Korovkin results are stated in weighted spaces. We prove a quantitative Voronovskaya-type theorem and present some results on the monotonic convergence of the sequence. Finally, we show a shape preserving property and further direct convergence theorems. Weighted modulus of continuity of first order and the notion of ϑ-convexity are used throughout the paper

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.

Quantitative q-Voronovskaya and q-Grüss–Voronovskaya-type results for q-Szász operators

2016 ◽  
Vol 23 (4) ◽  
pp. 459-468 ◽  
Author(s):  
Tuncer Acar
Keyword(s):  
Modulus Of Continuity ◽  
Pointwise Convergence ◽  
Type Theorem ◽  
Continuous Functions ◽  
Weighted Modulus Of Continuity ◽  
Szász Operators ◽  
Differentiable Functions ◽  
Voronovskaya Type Theorem ◽  
Weighted Modulus ◽  
Derivatives Of

AbstractIn the present paper, we mainly study quantitative Voronovskaya-type theorems for q-Szász operators defined in [20]. We consider weighted spaces of functions and the corresponding weighted modulus of continuity. We obtain the quantitative q-Voronovskaya-type theorem and the q-Grüss–Voronovskaya-type theorem in terms of the weighted modulus of continuity of q-derivatives of the approximated function. In this way, we either obtain the rate of pointwise convergence of q-Szász operators or we present these results for a subspace of continuous functions, although the classical ones are valid for differentiable functions.

scholarly journals Approximation for difference of Lupaş and some classical operators

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3311-3318
Author(s):  
Danyal Soybaş ◽  
Neha Malik
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Basis Functions ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus ◽  
The Difference ◽  
Kantorovich Operators

The approximation of difference of two linear positive operators having different basis functions is discussed in the present article. The quantitative estimates in terms of weighted modulus of continuity for the difference of Lupa? operators and the classical ones are obtained, viz. Lupa? and Baskakov operators, Lupa? and Sz?sz operators, Lupa? and Baskakov-Kantorovich operators, Lupa? and Sz?sz-Kantorovich operators.

scholarly journals The Approximation of Bivariate Blending Variant Szász Operators Based Brenke Type Polynomials

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Behar Baxhaku ◽  
Ramadan Zejnullahu ◽  
Artan Berisha
Keyword(s):  
Modulus Of Continuity ◽  
Weighted Space ◽  
Type Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weighted Modulus Of Continuity ◽  
Rate Of Approximation ◽  
Szász Operators ◽  
Weighted Modulus

We have constructed a new sequence of positive linear operators with two variables by using Szasz-Kantorovich-Chlodowsky operators and Brenke polynomials. We give some inequalities for the operators by means of partial and full modulus of continuity and obtain a Lipschitz type theorem. Furthermore, we study the convergence of Szasz-Kantorovich-Chlodowsky-Brenke operators in weighted space of function with two variables and estimate the rate of approximation in terms of the weighted modulus of continuity.

scholarly journals Quantitative estimates for Szász operators and its hybrid variant

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1107-1114
Author(s):  
Ekta Pandey
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Szász Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate the quantitative Voronovskaja type asymptotic formula for the Sz?sz-Baskakov operators and difference between Sz?sz-Mirakyan operators and the hybrid Sz?sz operators having weights of Baskakov basis in terms of the weighted modulus of continuity

scholarly journals Stancu-variant of generalized Baskakov operators

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2625-2632 ◽  
Author(s):  
Nadeem Rao ◽  
Abdul Wafi
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Modulus Of Smoothness ◽  
Order Of Approximation ◽  
Baskakov Operators ◽  
Direct Estimate ◽  
Voronovskaya Type Theorem

In the present paper, we introduce Stancu-variant of generalized Baskakov operators and study the rate of convergence using modulus of continuity, order of approximation for the derivative of function f . Direct estimate is proved using K-functional and Ditzian-Totik modulus of smoothness. In the last, we have proved Voronovskaya type theorem.

Dunkl generalization of Kantorovich type Szász–Mirakjan operators via q-calculus

2017 ◽  
Vol 10 (04) ◽  
pp. 1750077 ◽  
Author(s):  
M. Mursaleen ◽  
Md. Nasiruzzaman
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Second Order ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus

In this paper, we construct Kantorovich type Szász–Mirakjan operators generated by Dunkl generalization of the exponential function via [Formula: see text]-integers. We obtain some approximation results via well-known Korovkin’s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain the rate of convergence in terms of the classical, second-order, and weighted modulus of continuity.

scholarly journals Rate of convergence of Szász-beta operators based on q-integers

2017 ◽  
Vol 50 (1) ◽  
pp. 130-143 ◽  
Author(s):  
Pooja Gupta ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus ◽  
Lipschitz Type Maximal Function

Abstract The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

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 Approximation properties of the new type generalized Bernstein-Kantorovich operators

2021 ◽  
Vol 7 (3) ◽  
pp. 3826-3844
Author(s):  
Mustafa Kara ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Type Theorem ◽  
Numerical Results ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
New Type ◽  
Kantorovich Operators

<abstract><p>In this paper, we introduce new type of generalized Kantorovich variant of $ \alpha $-Bernstein operators and study their approximation properties. We obtain estimates of rate of convergence involving first and second order modulus of continuity and Lipschitz function are studied for these operators. Furthermore, we establish Voronovskaya type theorem of these operators. The last section is devoted to bivariate new type $ \alpha $-Bernstein-Kantorovich operators and their approximation behaviors. Also, some graphical illustrations and numerical results are provided.</p></abstract>

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