scholarly journals Complete asymptotic expansions related to conjecture on a Voronovskaja-type theorem

2018 ◽  
Vol 458 (1) ◽  
pp. 452-463 ◽  
Author(s):  
Ioan Gavrea ◽  
Mircea Ivan
Keyword(s):  
Asymptotic Expansions ◽  
Type Theorem ◽  
Voronovskaja Type Theorem

scholarly journals Generalized p,q-Gamma-type operators

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Wen-Tao Cheng ◽  
Qing-Bo Cai
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

In the present paper, the generalized p,q-gamma-type operators based on p,q-calculus are introduced. The moments and central moments are obtained, and some local approximation properties of these operators are investigated by means of modulus of continuity and Peetre K-functional. Also, the rate of convergence, weighted approximation, and pointwise estimates of these operators are studied. Finally, a Voronovskaja-type theorem is presented.

scholarly journals Dunkl generalization of q-Szász-Mirakjan operators which preserve x2

Filomat ◽  
2018 ◽  
Vol 32 (3) ◽  
pp. 733-747 ◽  
Author(s):  
Mohammad Mursaleen ◽  
Shagufta Rahman
Keyword(s):  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem

In the present paper we construct q-Sz?sz-Mirakjan operators generated by Dunkl generalization of the exponential function which preserve x2. We obtain some approximation results via universal Korovkin?s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain a Voronovskaja type theorem for these operators.

scholarly journals Approximation by Genuineq-Bernstein-Durrmeyer Polynomials in Compact Disks in the Caseq>1

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Nazim I. Mahmudov
Keyword(s):  
Open Problem ◽  
Analytic Functions ◽  
Type Theorem ◽  
Linear Operators ◽  
Explicit Formulas ◽  
Rate Of Approximation ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Compact Disks ◽  
Durrmeyer Polynomials

This paper deals with approximating properties of the newly definedq-generalization of the genuine Bernstein-Durrmeyer polynomials in the caseq>1, which are no longer positive linear operators onC0,1. Quantitative estimates of the convergence, the Voronovskaja-type theorem, and saturation of convergence for complex genuineq-Bernstein-Durrmeyer polynomials attached to analytic functions in compact disks are given. In particular, it is proved that, for functions analytic inz∈ℂ:z<R,R>q, the rate of approximation by the genuineq-Bernstein-Durrmeyer polynomialsq>1is of orderq−nversus1/nfor the classical genuine Bernstein-Durrmeyer polynomials. We give explicit formulas of Voronovskaja type for the genuineq-Bernstein-Durrmeyer forq>1. This paper represents an answer to the open problem initiated by Gal in (2013, page 115).

scholarly journals Approximation properties of modified Srivastava-Gupta operators based on certain parameter

2018 ◽  
Vol 38 (1) ◽  
pp. 41-53 ◽  
Author(s):  
Alok Kumar ◽  
Dr Vandana
Keyword(s):  
Maximal Function ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Voronovskaja Type Theorem ◽  
Direct Approximation ◽  
Lipschitz Type Maximal Function

In the present article, we give a modified form of generalized Srivastava-Gupta operators based on certain parameter which preserve the constant as well as linear functions. First, we estimate moments of the operators and then prove Voronovskaja type theorem. Next, direct approximation theorem, rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Then, we obtain point-wise estimate using the Lipschitz type maximal function. Finaly, we study the $A$-statistical convergence of these operators.

scholarly journals Voronovskaja-type theorem for certain GBS ope

2008 ◽  
Vol 43 (1) ◽  
pp. 179-184 ◽  
Author(s):  
Ovidiu T. Pop
Keyword(s):  
Type Theorem ◽  
Voronovskaja Type Theorem

scholarly journals On Stancu-Type Generalization of Modified p , q -Szász-Mirakjan-Kantorovich Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yong-Mo Hu ◽  
Wen-Tao Cheng ◽  
Chun-Yan Gui ◽  
Wen-Hui Zhang
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Pointwise Estimates ◽  
Approximation Properties ◽  
Voronovskaja Type Theorem ◽  
Kantorovich Operators

In the present article, we construct p , q -Szász-Mirakjan-Kantorovich-Stancu operators with three parameters λ , α , β . First, the moments and central moments are estimated. Then, local approximation properties of these operators are established via K -functionals and Steklov mean in means of modulus of continuity. Also, a Voronovskaja-type theorem is presented. Finally, the pointwise estimates, rate of convergence, and weighted approximation of these operators are studied.

scholarly journals Note on a Schurer-Stancu-type operator

2015 ◽  
Vol 24 (1) ◽  
pp. 61-67
Author(s):  
ADRIAN D. INDREA ◽  
◽  
ANAMARIA INDREA ◽  
PETRU I. BRAICA ◽  
◽  
...  
Keyword(s):  
Type Theorem ◽  
Type Operator ◽  
Test Functions ◽  
New Class ◽  
Voronovskaja Type Theorem

The aim of this paper is to introduce a class of operators of Schurer-Stancu-type with the property that the test functions e0 and e1 are reproduced. Also, in our approach, a theorem of error approximation and a Voronovskaja-type theorem for this operators are obtained. Finally, we study the convergence of the iterates for our new class of operators.

scholarly journals Approximation properties of multivariate exponential sampling series

2021 ◽  
Vol 13 (3) ◽  
pp. 666-675
Author(s):  
S. Kurşun ◽  
M. Turgay ◽  
O. Alagöz ◽  
T. Acar
Keyword(s):  
Asymptotic Behaviour ◽  
Type Theorem ◽  
Continuous Functions ◽  
Approximation Properties ◽  
Multivariate Functions ◽  
Voronovskaja Type Theorem ◽  
Sampling Series ◽  
The Family ◽  
Uniformly Continuous ◽  
Multivariate Exponential

In this paper, we generalize the family of exponential sampling series for functions of $n$ variables and study their pointwise and uniform convergence as well as the rate of convergence for the functions belonging to space of $\log$-uniformly continuous functions. Furthermore, we state and prove the generalized Mellin-Taylor's expansion of multivariate functions. Using this expansion we establish pointwise asymptotic behaviour of the series by means of Voronovskaja type theorem.

scholarly journals A new kind of Bi-variate $ \lambda $ -Bernstein-Kantorovich type operator with shifted knots and its associated GBS form

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Purshottam Narain Agrawal ◽  
Behar Baxhaku ◽  
Rahul Shukla
Keyword(s):  
Rate Of Convergence ◽  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Type Operator ◽  
Mixed Modulus Of Smoothness ◽  
Voronovskaja Type Theorem ◽  
Differentiable Functions ◽  
Mixed Modulus ◽  
Approximation Of A Function

<p style='text-indent:20px;'>In this paper, we introduce a bi-variate case of a new kind of <inline-formula><tex-math id="M1">\begin{document}$ \lambda $\end{document}</tex-math></inline-formula>-Bernstein-Kantorovich type operator with shifted knots defined by Rahman et al. [<xref ref-type="bibr" rid="b31">31</xref>]. The rate of convergence of the bi-variate operators is obtained in terms of the complete and partial moduli of continuity. Next, we give an error estimate in the approximation of a function in the Lipschitz class and establish a Voronovskaja type theorem. Also, we define the associated GBS(Generalized Boolean Sum) operators and study the degree of approximation of Bögel continuous and Bögel differentiable functions by these operators with the aid of the mixed modulus of smoothness. Finally, we show the rate of convergence of the bi-variate operators and their GBS case for certain functions by illustrative graphics and tables using MATLAB algorithms.</p>

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