scholarly journals A Kantorovich-Stancu Type Generalization of Szasz Operators including Brenke Type Polynomials

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Rabia Aktaş ◽  
Bayram Çekim ◽  
Fatma Taşdelen
Keyword(s):  
Type Theorem ◽  
Approximation Properties ◽  
Szász Operators ◽  
Voronovskaya Type Theorem

We introduce a Kantorovich-Stancu type modification of a generalization of Szasz operators defined by means of the Brenke type polynomials and obtain approximation properties of these operators. Also, we give a Voronovskaya type theorem for Kantorovich-Stancu type operators including Gould-Hopper polynomials.

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>

Generalized hybrid operators preserving exponential functions

2019 ◽  
Vol 12 (07) ◽  
pp. 1950089
Author(s):  
Deepika Agrawal ◽  
Vijay Gupta
Keyword(s):  
Asymptotic Formula ◽  
Comparative Study ◽  
Open Problem ◽  
Generating Functions ◽  
Graphical Representation ◽  
Type Theorem ◽  
Approximation Properties ◽  
Exponential Functions ◽  
Convergence Estimate ◽  
Voronovskaya Type Theorem

The present paper deals with the approximation properties of generalization of Lupaş–Păltănea’s operators preserving exponential functions. We obtain moments using the concept of moment generating functions and establish a Voronovskaya type theorem, uniform convergence estimate and also an asymptotic formula in quantitative sense. In the end we present comparative study through graphical representation and propose an open problem.

scholarly journals A new construction of Lupaş operators and its approximation properties

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mohd Qasim ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Qing-Bo Cai
Keyword(s):  
Uniform Approximation ◽  
Type Theorem ◽  
Local Approximation ◽  
Moduli Of Smoothness ◽  
Approximation Properties ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Lupaş Operators ◽  
New Construction ◽  
Weighted Moduli Of Smoothness

AbstractThe aim of this paper is to study a new generalization of Lupaş-type operators whose construction depends on a real-valued function ρ by using two sequences $u_{m} $ u m and $v_{m}$ v m of functions. We prove that the new operators provide better weighted uniform approximation over $[0,\infty )$ [ 0 , ∞ ) . In terms of weighted moduli of smoothness, we obtain degrees of approximation associated with the function ρ. Also, we prove Voronovskaya-type theorem, quantitative estimates for the local approximation.

scholarly journals Approximation by modified Păltănea operators

2020 ◽  
Vol 107 (121) ◽  
pp. 157-164
Author(s):  
Vijay Gupta ◽  
P.N. Agrawal
Keyword(s):  
Generating Function ◽  
Type Theorem ◽  
Moment Generating Function ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaya Type Theorem

We discuss some approximation properties of hybrid genuine operators. We find central moments using the concept of moment generating function. A quantitative Voronovskaya and Gruss-Voronovskaya type theorem are proven. Also, we obtain the degree of approximation of the considered operators by means of the second order Ditzian-Totik modulus of smoothness.

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.

scholarly journals Convergence of modified Szász-Mirakyan-Durrmeyer operators depending on certain parameters

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Mohd Qasim ◽  
Mohd Shanawaz Mansoori ◽  
Asif Khan ◽  
Zaheer Abbas ◽  
Mohammad Mursaleen
Keyword(s):  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Unbounded Function ◽  
Durrmeyer Operators ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Selection Of

<p style='text-indent:20px;'>Motivated by certain generalizations, in this paper we consider a new analogue of modified Szá sz-Mirakyan-Durrmeyer operators whose construction depends on a continuously differentiable, increasing and unbounded function <inline-formula><tex-math id="M1">\begin{document}$ \tau $\end{document}</tex-math></inline-formula> with extra parameters <inline-formula><tex-math id="M2">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>. Depending on the selection of <inline-formula><tex-math id="M4">\begin{document}$ \mu $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M5">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>, these operators are more flexible than the modified Szá sz-Mirakyan-Durrmeyer operators while retaining their approximation properties. For these operators we give weighted approximation, Voronovskaya type theorem and quantitative estimates for the local approximation.</p>

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 On approximation properties of Baskakov-Schurer-Szász-Stancu operators based on q-integers

Filomat ◽  
2018 ◽  
Vol 32 (4) ◽  
pp. 1359-1378 ◽  
Author(s):  
M. Mursaleen ◽  
A.A.H. Al-Abied ◽  
Khursheed Ansari
Keyword(s):  
Rate Of Convergence ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Approximation Properties ◽  
Stancu Operators ◽  
Voronovskaya Type Theorem ◽  
Lipschitz Type Maximal Function

In the present paper, we introduce Stancu type generalization of Baskakov-Schurer-Sz?sz operators based on the q-integers and investigate their approximation properties. We obtain rate of convergence, weighted approximation and Voronovskaya type theorem for new operators. Then we obtain a point-wise estimate using the Lipschitz type maximal function. Furthermore, we study A-statistical convergence of these operators and also, in order to obtain a better approximation.

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.

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.

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