scholarly journals Quantitative estimates for the Lupaş q-analogue of the Bernstein operator

2011 ◽  
Vol 44 (1) ◽  
Author(s):  
Zoltán Finta
Keyword(s):  
Modulus Of Smoothness ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Quantitative Estimates ◽  
Quantitative Results

AbstractWe establish quantitative results for the approximation properties of the q-analogue of the Bernstein operator defined by Lupaş in 1987 and for the approximation properties of the limit Lupaş operator introduced by Ostrovska in 2006, via Ditzian-Totik modulus of smoothness. Our results are local and global approximation theorems.

scholarly journals Approximation by Parametric Extension of Szász-Mirakjan-Kantorovich Operators Involving the Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Rate Of Convergence ◽  
Weighted Space ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Appell Polynomials ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Dunkl Analogue ◽  
Kantorovich Operators

The purpose of this article is to introduce a Kantorovich variant of Szász-Mirakjan operators by including the Dunkl analogue involving the Appell polynomials, namely, the Szász-Mirakjan-Jakimovski-Leviatan-type positive linear operators. We study the global approximation in terms of uniform modulus of smoothness and calculate the local direct theorems of the rate of convergence with the help of Lipschitz-type maximal functions in weighted space. Furthermore, the Voronovskaja-type approximation theorems of this new operator are also presented.

scholarly journals Construction of Stancu-Type Bernstein Operators Based on Bézier Bases with Shape Parameter λ

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 316 ◽  
Author(s):  
Hari Srivastava ◽  
Faruk Özger ◽  
S. Mohiuddine
Keyword(s):  
Uniform Convergence ◽  
Shape Parameter ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Bernstein Operators ◽  
Global Approximation ◽  
Approximation Result ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Direct Approximation

We construct Stancu-type Bernstein operators based on Bézier bases with shape parameter λ ∈ [ - 1 , 1 ] and calculate their moments. The uniform convergence of the operator and global approximation result by means of Ditzian-Totik modulus of smoothness are established. Also, we establish the direct approximation theorem with the help of second order modulus of smoothness, calculate the rate of convergence via Lipschitz-type function, and discuss the Voronovskaja-type approximation theorems. Finally, in the last section, we construct the bivariate case of Stancu-type λ -Bernstein operators and study their approximation behaviors.

scholarly journals Blending type Approximations by Kantorovich variant of α-Schurer operators

2021 ◽  
Author(s):  
Nadeem Rao ◽  
Pradeep Malik ◽  
Mamta Rani
Keyword(s):  
Numerical Analysis ◽  
Modulus Of Smoothness ◽  
Second Order ◽  
Weight Functions ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Global Approximation ◽  
Measurable Functions ◽  
Two Parameters ◽  
Kantorovich Operators

In the present manuscript, we present a new sequence of operators, i:e:, -Bernstein-Schurer-Kantorovich operators depending on two parameters 2 [0; 1] and > 0 foe one and two variables to approximate measurable functions on [0:1+q]; q > 0. Next, we give basic results and discuss the rapidity of convergence and order of approximation for univariate and bivariate of these sequences in their respective sections . Further, Graphical and numerical analysis are presented. Moreover, local and global approximation properties are discussed in terms of rst and second order modulus of smoothness, Peetre’s K-functional and weight functions for these sequences in dierent spaces of functions.

Korovkin-type theorems and applications

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Nazim Mahmudov
Keyword(s):  
Type Theorem ◽  
Linear Operators ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Korovkin Type Theorem ◽  
Quantitative Results ◽  
Korovkin Type Theorems

AbstractLet {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.

I-approximation properties of certain class of linear positive operators

2011 ◽  
Vol 48 (2) ◽  
pp. 205-219
Author(s):  
Nazim Mahmudov ◽  
Mehmet Özarslan ◽  
Pembe Sabancigil
Keyword(s):  
Modulus Of Smoothness ◽  
Positive Operators ◽  
Approximation Properties ◽  
Global Approximation ◽  
Linear Positive Operators ◽  
Durrmeyer Operators

In this paper we studyI-approximation properties of certain class of linear positive operators. The two main tools used in this paper areI-convergence and Ditzian-Totik modulus of smoothness. Furthermore, we defineq-Lupaş-Durrmeyer operators and give local and global approximation results for such operators.

scholarly journals Approximation theorems for q-Bernstein-Kantorovich operators

Filomat ◽  
2013 ◽  
Vol 27 (4) ◽  
pp. 721-730 ◽  
Author(s):  
Nazim Mahmudov ◽  
Pembe Sabancigil
Keyword(s):  
Type Theorem ◽  
Approximation Properties ◽  
Global Approximation ◽  
Approximation Theorems ◽  
Voronovskaja Type Theorem ◽  
Kantorovich Operators

In the present paper we introduce a q-analogue of the Bernstein-Kantorovich operators and investigate their approximation properties. We study local and global approximation properties and Voronovskaja type theorem for the q-Bernstein-Kantorovich operators in case 0 < q < 1.

scholarly journals Approximation by limit q-Bernstein operator

2013 ◽  
Vol 5 (1) ◽  
pp. 39-46
Author(s):  
Zoltán Finta
Keyword(s):  
Modulus Of Smoothness ◽  
Second Order ◽  
Bernstein Operator ◽  
Quantitative Estimates

Abstract We establish quantitative estimates for the limit q-Bernstein operator introduced in [3], via the second order Ditzian-Totik modulus of smoothness.

scholarly journals Quantitative Estimates for Nonlinear Sampling Kantorovich Operators

2021 ◽  
Vol 76 (2) ◽  
Author(s):  
Nursel Çetin ◽  
Danilo Costarelli ◽  
Gianluca Vinti
Keyword(s):  
Orlicz Spaces ◽  
General Setting ◽  
Modulus Of Smoothness ◽  
Direct Approach ◽  
Order Of Approximation ◽  
Lipschitz Classes ◽  
General Frame ◽  
Quantitative Estimates ◽  
Nonlinear Sampling ◽  
Kantorovich Operators

AbstractIn this paper, we establish quantitative estimates for nonlinear sampling Kantorovich operators in terms of the modulus of smoothness in the setting of Orlicz spaces. This general frame allows us to directly deduce some quantitative estimates of approximation in $$L^{p}$$ L p -spaces, $$1\le p<\infty $$ 1 ≤ p < ∞ , and in other well-known instances of Orlicz spaces, such as the Zygmung and the exponential spaces. Further, the qualitative order of approximation has been obtained assuming f in suitable Lipschitz classes. The above estimates achieved in the general setting of Orlicz spaces, have been also improved in the $$L^p$$ L p -case, using a direct approach suitable to this context. At the end, we consider the particular cases of the nonlinear sampling Kantorovich operators constructed by using some special kernels.

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