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 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 On a Durrmeyer-type modification of the Exponential sampling series

2020 ◽  
Author(s):  
Carlo Bardaro ◽  
Ilaria Mantellini
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Convergence Properties ◽  
Sampling Series ◽  
Quantitative Results ◽  
Uniformly Continuous

Abstract In this paper we introduce the exponential sampling Durrmeyer series. We discuss pointwise and uniform convergence properties and an asymptotic formula of Voronovskaja type. Quantitative results are given, using the usual modulus of continuity for uniformly continuous functions. Some examples are also described.

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 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 Approximation by pseudo-linear discrete operators

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
İsmail Aslan ◽  
Türkan Yeliz Gökçer
Keyword(s):  
Error Estimation ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Discrete Operator ◽  
Generalized Sampling ◽  
Sampling Series ◽  
Discrete Operators ◽  
Generator Function ◽  
Uniformly Continuous

<p style='text-indent:20px;'>In this note, we construct a pseudo-linear kind discrete operator based on the continuous and nondecreasing generator function. Then, we obtain an approximation to uniformly continuous functions through this new operator. Furthermore, we calculate the error estimation of this approach with a modulus of continuity based on a generator function. The obtained results are supported by visualizing with an explicit example. Finally, we investigate the relation between discrete operators and generalized sampling series.</p>

scholarly journals Approximation properties of mixed sampling-Kantorovich operators

2020 ◽  
Vol 115 (1) ◽  
Author(s):  
Laura Angeloni ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Type Theorem ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Voronovskaja Type Theorem ◽  
Quantitative Estimates ◽  
Kantorovich Operators

Abstract In the present paper we study the pointwise and uniform convergence properties of a family of multidimensional sampling Kantorovich type operators. Moreover, besides convergence, quantitative estimates and a Voronovskaja type theorem have been established.

scholarly journals Some approximation properties of new $( p,q ) $-analogue of Balázs–Szabados operators

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Hayatem Hamal ◽  
Pembe Sabancigil
Keyword(s):  
Fourth Order ◽  
Type Theorem ◽  
Local Approximation ◽  
Second Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Voronovskaja Type Theorem

AbstractIn this paper, a new $( p,q ) $ ( p , q ) -analogue of the Balázs–Szabados operators is defined. Moments up to the fourth order are calculated, and second order and fourth order central moments are estimated. Local approximation properties of the operators are examined and a Voronovskaja type theorem is given.

scholarly journals Approximation properties of modified q-gamma operators preserving linear functions

Filomat ◽  
2020 ◽  
Vol 34 (5) ◽  
pp. 1601-1609
Author(s):  
Wen-Tao Cheng ◽  
Wen-Hui Zhang ◽  
Jing Zhang
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Linear Functions ◽  
Approximation Properties ◽  
Gamma Functions ◽  
Voronovskaja Type Theorem

In this paper, we introduce the q-analogue of modified Gamma operators preserving linear functions. We establish the moments of the operators using the q-Gamma functions. Next, some local approximation for the above operators are discussed. Also, the rate of convergence and weighted approximation by these operators in terms of modulus of continuity are studied. Furthermore, we obtain the Voronovskaja type theorem.

scholarly journals Approximation Properties of Generalized λ -Bernstein–Stancu-Type Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Qing-Bo Cai ◽  
Gülten Torun ◽  
Ülkü Dinlemez Kantar
Keyword(s):  
Asymptotic Behavior ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Type Theorem ◽  
Approximation Properties ◽  
Numerical Examples ◽  
Korovkin Type Approximation Theorem ◽  
Type Approximation ◽  
Voronovskaja Type Theorem

The present study introduces generalized λ -Bernstein–Stancu-type operators with shifted knots. A Korovkin-type approximation theorem is given, and the rate of convergence of these types of operators is obtained for Lipschitz-type functions. Then, a Voronovskaja-type theorem was given for the asymptotic behavior for these operators. Finally, numerical examples and their graphs were given to demonstrate the convergence of G m , λ α , β f , x to f x with respect to m values.

scholarly journals Lupaş post quantum Bernstein operators over arbitrary compact intervals

2021 ◽  
Vol 13 (3) ◽  
pp. 734-749
Author(s):  
A. Khan ◽  
M. Iliyas ◽  
M.S. Mansoori ◽  
M. Mursaleen
Keyword(s):  
Type Theorem ◽  
Continuous Functions ◽  
General Situation ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Scale Invariant ◽  
Korovkin Type Theorem ◽  
Computational Point ◽  
Bounded Interval ◽  
Bernstein Bases

This paper deals with Lupaş post quantum Bernstein operators over arbitrary closed and bounded interval constructed with the help of Lupaş post quantum Bernstein bases. Due to the property that these bases are scale invariant and translation invariant, the derived results on arbitrary intervals are important from computational point of view. Approximation properties of Lupaş post quantum Bernstein operators on arbitrary compact intervals based on Korovkin type theorem are studied. More general situation along all possible cases have been discussed favouring convergence of sequence of Lupaş post quantum Bernstein operators to any continuous function defined on compact interval. Rate of convergence by modulus of continuity and functions of Lipschitz class are computed. Graphical analysis has been presented with the help of MATLAB to demonstrate approximation of continuous functions by Lupaş post quantum Bernstein operators on different compact intervals.

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