scholarly journals Approximation of Functions by Dunkl-Type Generalization of Szász-Durrmeyer Operators Based on p , q -Integers

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Abdullah Alotaibi
Keyword(s):  
Exponential Function ◽  
Weighted Spaces ◽  
Approximation Of Functions ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators ◽  
Direct Results

In this article, our main purpose is to define the p , q -variant of Szász-Durrmeyer type operators with the help of Dunkl generalization generated by an exponential function. We estimate moments and establish some direct results of the aforementioned operators. Moreover, we establish some approximation results in weighted spaces.

scholarly journals A genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2611-2623 ◽  
Author(s):  
Trapti Neer ◽  
P.N. Agrawal
Keyword(s):  
Approximation Theorem ◽  
Local Approximation ◽  
Modulus Of Smoothness ◽  
Basis Functions ◽  
Global Approximation ◽  
Approximation Of Functions ◽  
Moment Estimates ◽  
Durrmeyer Type Operators ◽  
Direct Results ◽  
Classical Modulus

In this paper, we construct a genuine family of Bernstein-Durrmeyer type operators based on Polya basis functions. We establish some moment estimates and the direct results which include global approximation theorem in terms of classical modulus of continuity, local approximation theorem in terms of the second order Ditizian-Totik modulus of smoothness, Voronovskaya-type asymptotic theorem and a quantitative estimate of the same type. Lastly, we study the approximation of functions having a derivative of bounded variation.

scholarly journals Approximation by Jakimovski-Leviatan-Stancu-Durrmeyer type operators

Filomat ◽  
2019 ◽  
Vol 33 (6) ◽  
pp. 1517-1530 ◽  
Author(s):  
M. Mursaleen ◽  
Shagufta Rahman ◽  
Khursheed Ansari
Keyword(s):  
Upper Bound ◽  
Simultaneous Approximation ◽  
Approximation Theorem ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Durrmeyer Operators ◽  
Durrmeyer Type Operators

In the present paper, we introduce Stancu type modification of Jakimovski-Leviatan-Durrmeyer operators. First, we estimate moments of these operators. Next, we study the problem of simultaneous approximation by these operators. An upper bound for the approximation to rth derivative of a function by these operators is established. Furthermore, we obtain A-statistical approximation properties of these operators with the help of universal korovkin type statistical approximation theorem.

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.

Approximation of functions of bounded variation by integrated Meyer-König and Zeller operators of finite type

2012 ◽  
Vol 49 (2) ◽  
pp. 254-268
Author(s):  
Tiberiu Trif
Keyword(s):  
Rate Of Convergence ◽  
Finite Type ◽  
Bounded Variation ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Approximation Of Functions ◽  
Durrmeyer Operators

I. Gavrea and T. Trif [Rend. Circ. Mat. Palermo (2) Suppl. 76 (2005), 375–394] introduced a class of Meyer-König-Zeller-Durrmeyer operators “of finite type” and investigated the rate of convergence of these operators for continuous functions. In the present paper we study the approximation of functions of bounded variation by means of these operators.

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.

Genuine link Baskakov–Durrmeyer operators

2018 ◽  
Vol 25 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Vijay Gupta ◽  
Neha Malik
Keyword(s):  
Asymptotic Formula ◽  
Simultaneous Approximation ◽  
Weighted Approximation ◽  
Approximation Result ◽  
Durrmeyer Operators ◽  
Direct Results

AbstractIn the present paper, we propose a sequence of generalized genuine Baskakov–Durrmeyer-type link operators. In terms of ordinary approximation, we estimate local and global direct results and also study the weighted approximation result. In terms of simultaneous approximation, we establish an asymptotic formula of Voronovskaja kind. In the last section, we prove convergence in{L_{p}}-norm.

scholarly journals Better approximation of functions by genuine Bernstein-Durrmeyer type operators

2019 ◽  
Vol 35 (2) ◽  
pp. 125-136
Author(s):  
ANA MARIA ACU ◽  
P. N. AGRAWAL ◽  
◽  
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Of Functions ◽  
Numerical Examples ◽  
Durrmeyer Operator ◽  
Durrmeyer Type Operators ◽  
Theoretical Results ◽  
Second Modulus Of Continuity

The main object of this paper is to construct a new genuine Bernstein-Durrmeyer type operators which have better features than the classical one. Some direct estimates for the modified genuine Bernstein-Durrmeyer operator by means of the first and second modulus of continuity are given. An asymptotic formula for the new operator is proved. Finally, some numerical examples with illustrative graphics have been added to validate the theoretical results and also compare the rate of convergence.

On Iterative Combination of Modified Bernstein-Type Polynomials

2008 ◽  
Vol 15 (4) ◽  
pp. 591-600
Author(s):  
P. N. Agrawal ◽  
Asha Ram Gairola ◽  
Vijay Gupta
Keyword(s):  
Linear Functions ◽  
Bernstein Type ◽  
Durrmeyer Operators ◽  
New Type ◽  
Direct Results

Abstract The paper deals with some direct results on ordinary and simultaneous approximations for iterative combinations of a new type of Bernstein–Durrmeyer operators. Gupta and Vasishtha [Math. Comput. Modelling 39: 521–527, 2004] have recently claimed that iterative combinations can be applied only for those operators for which 𝑡 maps exactly to 𝑥. Here we disagree with their claim and state that iterative combinations can be applied for other operators which do not reproduce linear functions either.

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