scholarly journals Generalized Bernstein type operators on unbounded interval and some approximation properties

Filomat ◽  
2019 ◽  
Vol 33 (9) ◽  
pp. 2797-2808 ◽  
Author(s):  
Mohd Ahasan ◽  
Faisal Khan ◽  
Mohammad Mursaleen
Keyword(s):  
Exponential Function ◽  
Infinite Interval ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Unbounded Interval ◽  
New Family

In the present paper, we construct a new family of Bernstein type operators on infinite interval by using exponential function ax. We study some approximation results for these new operators on the interval [0,1).

The Dunkl generalization of Stancu type q-Szasz-Mirakjan-Kantorovich operators and some approximation results

2018 ◽  
Vol 34 (3) ◽  
pp. 363-370
Author(s):  
M. MURSALEEN ◽  
◽  
MOHD. AHASAN ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Second Order ◽  
Lipschitz Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Kantorovich Operators ◽  
Korovkin’S Theorem

In this paper, a Dunkl type generalization of Stancu type q-Szasz-Mirakjan-Kantorovich positive linear operators ´ of the exponential function is introduced. With the help of well-known Korovkin’s theorem, some approximation properties and also the rate of convergence for these operators in terms of the classical and second-order modulus of continuity, Peetre’s K-functional and Lipschitz functions are investigated.

scholarly journals On the Approximation Properties of q − Analogue Bivariate λ -Bernstein Type Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Edmond Aliaga ◽  
Behar Baxhaku
Keyword(s):  
Type Theorem ◽  
Degree Of Approximation ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Matlab Software ◽  
Type Space ◽  
Mixed Modulus Of Smoothness ◽  
Mixed Modulus ◽  
Boolean Sum

In this article, we establish an extension of the bivariate generalization of the q -Bernstein type operators involving parameter λ and extension of GBS (Generalized Boolean Sum) operators of bivariate q -Bernstein type. For the first operators, we state the Volkov-type theorem and we obtain a Voronovskaja type and investigate the degree of approximation by means of the Lipschitz type space. For the GBS type operators, we establish their degree of approximation in terms of the mixed modulus of smoothness. The comparison of convergence of the bivariate q -Bernstein type operators based on parameters and its GBS type operators is shown by illustrative graphics using MATLAB software.

Sinc Approximation

1995 ◽  
Author(s):  
Marek A. Kowalski ◽  
Krzystof A. Sikorski ◽  
Frank Stenger
Keyword(s):  
Boundary Layer ◽  
Infinite Interval ◽  
Sinc Approximation ◽  
End Point ◽  
New Family ◽  
Methods Of Approximation

Sine methods are a new family of self-contained methods of approximation, which have several advantages over classical methods of approximation in the case of the presence of end-point singularities, in the case when we have a semi-infinite or infinite interval of approximation, or in the case of the presence of a boundary layer situation.

scholarly journals Approximation properties of (p, q)-Bernstein type operators

2016 ◽  
Vol 8 (2) ◽  
pp. 222-232 ◽  
Author(s):  
Zoltán Finta
Keyword(s):  
Rate Of Convergence ◽  
Quantitative Estimation ◽  
Bernstein Operators ◽  
Bernstein Operator ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Direct Approximation

AbstractWe introduce a new generalization of the q-Bernstein operators involving (p, q)-integers, and we establish some direct approximation results. Further, we define the limit (p, q)-Bernstein operator, and we obtain its estimation for the rate of convergence. Finally, we introduce the (p, q)-Kantorovich type operators, and we give a quantitative estimation.

Error estimation by new family of generalized Bernstein type polynomial

2020 ◽  
Author(s):  
R. K. Mishra ◽  
Sudesh Kumar Garg ◽  
Rashmi Mishra
Keyword(s):  
Error Estimation ◽  
Bernstein Type ◽  
New Family

scholarly journals On Some Approximation Properties for a Sequence of λ-Bernstein Type Operators

2021 ◽  
pp. 4903-4915
Author(s):  
Ali Jassim Muhammad ◽  
Asma Jaber
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Convergence Theorem ◽  
Recurrence Relations ◽  
Bernstein Polynomials ◽  
Negative Integer ◽  
Asymptotic Formulas ◽  
Order Moment ◽  
Approximation Properties ◽  
Bernstein Type

In 2010, Long and Zeng introduced a new generalization of the Bernstein polynomials that depends on a parameter  and called -Bernstein polynomials. After that, in 2018, Lain and Zhou studied the uniform convergence for these -polynomials and obtained a Voronovaskaja-type asymptotic formula in ordinary approximation. This paper studies the convergence theorem and gives two Voronovaskaja-type asymptotic formulas of the sequence of -Bernstein polynomials in both ordinary and simultaneous approximations. For this purpose, we discuss the possibility of finding the recurrence relations of the -th order moment for these polynomials and evaluate the values of -Bernstein for the functions ,  is a non-negative integer

scholarly journals Approximation Properties of Recursively Defined Bernstein-Type Operators

1996 ◽  
Vol 87 (3) ◽  
pp. 243-269 ◽  
Author(s):  
Michele Campiti ◽  
Giorgio Metafune
Keyword(s):  
Approximation Properties ◽  
Bernstein Type

Bernstein-type operators which preserve exactly two test functions

2013 ◽  
Vol 50 (4) ◽  
pp. 393-405 ◽  
Author(s):  
Ovidiu Pop ◽  
Dan Bǎrbosu ◽  
Petru Braica
Keyword(s):  
Convergence Theorem ◽  
General Class ◽  
Type Theorem ◽  
Positive Operators ◽  
Bernstein Operators ◽  
Test Functions ◽  
Approximation Properties ◽  
Bernstein Type ◽  
Voronovskaja Type Theorem

A general class of linear and positive operators dened by nite sum is constructed. Some of their approximation properties, including a convergence theorem and a Voronovskaja-type theorem are established. Next, the operators of the considered class which preserve exactly two test functions from the set {e0, e1, e2} are determined. It is proved that the test functions e0 and e1 are preserved only by the Bernstein operators, the test functions e0 and e2 only by the King operators while the test functions e1 and e2 only by the operators recently introduced by P. I. Braica, O. T. Pop and A. D. Indrea in [4].

scholarly journals Approximation by New Family of Modified Bernstein Type Polynomials

2019 ◽  
Vol 9 (2) ◽  
pp. 4020-4022
Keyword(s):  
Approximation Methods ◽  
Bernstein Type ◽  
New Family ◽  
Laplace Formula

In the present paper our main aim is to use the approximation methods to express the Laplace formula of theory of probability by new family of modified Bernstein Type Polynomials defined for the function f(u) of .

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