scholarly journals The q -Chlodowsky and q -Szasz-Durrmeyer Hybrid Operators on Weighted Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Harun Çiçek ◽  
Aydın İzgi
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Weighted Spaces ◽  
Moduli Of Continuity ◽  
Approximation Properties ◽  
New Type

The main aim of this article is to introduce a new type of q -Chlodowsky and q -Szasz-Durrmeyer hybrid operators on weighted spaces. To this end, we give approximation properties of the modified new q -Hybrid operators. Moreover, in the weighted spaces, we examine the rate of convergence of the modified new q -Hybrid operators by means of moduli of continuity. In addition, we derive Voronovskaja’s type asymptotic formula for the related operators.

scholarly journals Some Approximation Properties of Modified Jain-Beta Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Prashantkumar Patel
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Basis Function ◽  
Function Approximation ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weight Functions ◽  
Approximation Properties

Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters α, β, and γ and discuss Voronovskaja asymptotic formula.

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>

scholarly journals Approximation Properties of Certain Summation Integral Type Operators

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
P. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Positive Operators ◽  
Inverse Theorem ◽  
Approximation Properties ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Direct Results

AbstractIn the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

scholarly journals Bivariate Positive Operators in Polynomial Weighted Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Octavian Agratini
Keyword(s):  
Rate Of Convergence ◽  
Positive Operators ◽  
Weighted Spaces ◽  
Two Dimensional ◽  
Approximation Properties ◽  
Special Cases ◽  
Finite Sums

This paper aims to two-dimensional extension of some univariate positive approximation processes expressed by series. To be easier to use, we also modify this extension into finite sums. With respect to these two new classes designed, we investigate their approximation properties in polynomial weighted spaces. The rate of convergence is established, and special cases of our construction are highlighted.

Some approximation properties of a kind of (p, q)-Phillips operators

2019 ◽  
Vol 69 (6) ◽  
pp. 1381-1394
Author(s):  
Wentao Cheng ◽  
Chunyan Gui ◽  
Yongmo Hu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Phillips Operators

Abstract In this paper, a kind of new analogue of Phillips operators based on (p, q)-integers is introduced. The moments of the operators are established. Then some local approximation for the above operators is discussed. Also, the rate of convergence and weighted approximation by these operators by means of modulus of continuity are studied. Furthermore, the Voronovskaja type asymptotic formula is investigated.

scholarly journals APPROXIMATION PROPERTIES OF MODIFIED BASKAKOV GAMMA OPERATORS

2021 ◽  
pp. 125
Author(s):  
Seda Arpagus ◽  
Ali Olgun
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Gamma Operator ◽  
Voronovskaya Type Theorem

In this present paper, we study an approximation properties of modified Baskakov-Gamma operator. Using Korovkin type theorem we first give approximation properties of this operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we give an approximation properties of weighted spaces. Finally, we study the Voronovskaya type theorem of this operator.

On Approximation Properties of a New Type of Bernstein-Durrmeyer Operators

2015 ◽  
Vol 65 (5) ◽  
Author(s):  
Tuncer Acar ◽  
Ali Aral ◽  
Vijay Gupta
Keyword(s):  
Asymptotic Formula ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Hypergeometric Series ◽  
Approximation Properties ◽  
Global Approximation ◽  
Durrmeyer Operators ◽  
New Type

AbstractThe present paper deals with a new type of Bernstein-Durrmeyer operators on mobile interval. First, we represent the operators in terms of hypergeometric series. We also establish local and global approximation results for these operators in terms of modulus of continuity. We obtain an asymptotic formula for these operators and in the last section we present better error estimation for the operators using King type approach

scholarly journals On approximation of Bernstein–Chlodowsky–Gadjiev type operators that fix $e^{-2x}$

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Feyza Tanberk Okumuş ◽  
Mahmut Akyiğit ◽  
Khursheed J. Ansari ◽  
Fuat Usta
Keyword(s):  
Rate Of Convergence ◽  
Numerical Experiments ◽  
Type Theorem ◽  
Function Spaces ◽  
Moduli Of Continuity ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
Different Types ◽  
Theoretical Results

Abstractthat fix the function $e^{-2x} $ e − 2 x for $x\geq 0 $ x ≥ 0 . Then, we provide the approximation properties of these newly defined operators for different types of function spaces. In addition, we focus on the rate of convergence utilizing appropriate moduli of continuity. Then, we provide the Voronovskaya-type theorem for these new operators. Finally, in order to validate our theoretical results, we provide some numerical experiments that are produced by a MATLAB complier.

scholarly journals Approximation properties of modified Jain-Gamma operators

2021 ◽  
Vol 13 (3) ◽  
pp. 651-665
Author(s):  
S. Erdogan ◽  
A. Olgun
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Gamma Operator ◽  
Voronovskaya Type Theorem

In the present paper, we study some approximation properties of a modified Jain-Gamma operator. Using Korovkin type theorem, we first give approximation properties of such operator. Secondly, we compute the rate of convergence of this operator by means of the modulus of continuity and we present approximation properties of weighted spaces. Finally, we obtain the Voronovskaya type theorem of this operator.

scholarly journals Approximation Properties of p , q -Szász-Mirakjan-Durrmeyer Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Zhi-Peng Lin ◽  
Wen-Tao Cheng ◽  
Xiao-Wei Xu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Gamma Function ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Central Moments ◽  
Durrmeyer Operators

In this article, we introduce a new Durrmeyer-type generalization of p , q -Szász-Mirakjan operators using the p , q -gamma function of the second kind. The moments and central moments are obtained. Then, the Voronovskaja-type asymptotic formula is investigated and point-wise estimates of these operators are studied. Also, some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K -functional. Finally, the rate of convergence and weighted approximation of these operators are presented.

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