King type generalization of Baskakov operators based on (𝑝, 𝑞) calculus with better approximation properties

Analysis ◽  
2020 ◽  
Vol 40 (4) ◽  
pp. 163-173
Author(s):  
Lakshmi Narayan Mishra ◽  
Shikha Pandey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Modulus Of Continuity ◽  
Research Area ◽  
Positive Operators ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Result ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Test Function

AbstractApproximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)-Baskakov operators, which reproduce the test function x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.

Statistical approximation properties of modified Durrmeyer q-Baskakov type operators with two parameters α and β

2016 ◽  
Vol 10 (02) ◽  
pp. 1750028
Author(s):  
Vishnu Narayan Mishra ◽  
Preeti Sharma
Keyword(s):  
Modulus Of Continuity ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Approximation Theorem ◽  
Rates Of Convergence ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Baskakov Operators ◽  
Two Parameters ◽  
Lipschitz Type Maximal Function

The main aim of this study is to obtain statistical approximation properties of these operators with the help of the Korovkin type statistical approximation theorem. Rates of statistical convergence by means of the modulus of continuity and the Lipschitz type maximal function are also established. Our results show that rates of convergence of our operators are at least as fast as classical Durrmeyer type modified Baskakov operators.

q -Laguerre type linear positive operators

2007 ◽  
Vol 44 (1) ◽  
pp. 65-80 ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Lipschitz Class ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
The Difference

The main object of this paper is to define the q -Laguerre type positive linear operators and investigate the approximation properties of these operators. The rate of convegence of these operators are studied by using the modulus of continuity, Peetre’s K -functional and Lipschitz class functional. The estimation to the difference | Mn +1, q ( ƒ ; χ )− Mn , q ( ƒ ; χ )| is also obtained for the Meyer-König and Zeller operators based on the q -integers [2]. Finally, the r -th order generalization of the q -Laguerre type operators are defined and their approximation properties and the rate of convergence of this r -th order generalization are also examined.

On positive operators involving a certain class of generating functions

2004 ◽  
Vol 41 (4) ◽  
pp. 415-429 ◽  
Author(s):  
O. Doğru ◽  
M. A. Özarslan ◽  
F. Taşdelen
Keyword(s):  
Differential Equations ◽  
Modulus Of Continuity ◽  
Generating Functions ◽  
Order Of Convergence ◽  
Positive Operators ◽  
Approximation Properties ◽  
Korovkin Theorem ◽  
Linear Positive Operators ◽  
General Sequence ◽  
The Korovkin Theorem

In this paper we introduced the general sequence of linear positive operators via generating functions. Approximation properties of these operators are obtained with the help of the Korovkin Theorem. The order of convergence of these operators computed by means of modulus of continuity Peetre’s K-furictiorial and the elements of the usual Lipschitz class. Also we introduce the r-th order generalization of these operators and we evaluate this generalization by the operators defined in this paper. Finally we give some applications to differential equations.

Iterative combinations for Srivastava–Gupta operators

2020 ◽  
pp. 2150108
Author(s):  
Prerna Maheshwari Sharma
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Positive Operators ◽  
Integral Type ◽  
Linear Positive Operators ◽  
General Family ◽  
Special Cases

In the year 2003, Srivastava–Gupta proposed a general family of linear positive operators, having some well-known operators as special cases. They investigated and established the rate of convergence of these operators for bounded variations. In the last decade for modified form of Srivastava–Gupta operators, several other generalizations also have been discussed. In this paper, we discuss the generalized modified Srivastava–Gupta operators considered in [H. M. Srivastava and V. Gupta, A certain family of summation-integral type operators, Math. Comput. Modelling 37(12–13) (2003) 1307–1315], by using iterative combinations in ordinary and simultaneous approximation. We may have better approximation in higher order of modulus of continuity for these operators.

scholarly journals TheΘ-transformation of certain positive linear operators

1996 ◽  
Vol 19 (4) ◽  
pp. 667-678 ◽  
Author(s):  
Aleandru Lupaş ◽  
Detlef H. Mache
Keyword(s):  
Construction Method ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Order Of Approximation ◽  
Linear Positive Operators

The intention of this paper is to describe a construction method for a new sequence of linear positive operators, which enables us to get a pointwise order of approximation regarding the polynomial summator operators which have “best” properties of approximation.

scholarly journals Approximation by Certain Linear Positive Operators of Two Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Afşin Kürşat Gazanfer ◽  
İbrahim Büyükyazıcı
Keyword(s):  
Convergence Rate ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Compact Set ◽  
Approximation Properties ◽  
Linear Positive Operators ◽  
Functions Of Two Variables

We introduce positive linear operators which are combined with the Chlodowsky and Szász type operators and study some approximation properties of these operators in the space of continuous functions of two variables on a compact set. The convergence rate of these operators are obtained by means of the modulus of continuity. And we also obtain weighted approximation properties for these positive linear operators in a weighted space of functions of two variables and find the convergence rate for these operators by using the weighted modulus of continuity.

scholarly journals Approximation for difference of Lupaş and some classical operators

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3311-3318
Author(s):  
Danyal Soybaş ◽  
Neha Malik
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Basis Functions ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus ◽  
The Difference ◽  
Kantorovich Operators

The approximation of difference of two linear positive operators having different basis functions is discussed in the present article. The quantitative estimates in terms of weighted modulus of continuity for the difference of Lupa? operators and the classical ones are obtained, viz. Lupa? and Baskakov operators, Lupa? and Sz?sz operators, Lupa? and Baskakov-Kantorovich operators, Lupa? and Sz?sz-Kantorovich operators.

scholarly journals The (p; q)-Bernstein-Stancu operator of rough statistical convergence on triple sequence

2019 ◽  
Vol 38 (7) ◽  
pp. 125-136
Author(s):  
Ayhan Esi ◽  
M. Kemal Ozdemir ◽  
Nagarajan Subramanian
Keyword(s):  
Error Bound ◽  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Stancu Operators

In the paper, we investigate rough statistical approximation properties of (p; q)-analogue of Bernstein-Stancu Operators. We study approximation properties based on rough statistical convergence. We also study error bound using modulus of continuity.

A sequence of positive linear operators related to powered Baskakov basis

2019 ◽  
Vol 35 (1) ◽  
pp. 51-58
Author(s):  
ADRIAN HOLHOS ◽  
Keyword(s):  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Properties ◽  
Type Result ◽  
Baskakov Operators ◽  
Better Than

In this paper we study some approximation properties of a sequence of positive linear operators defined by means of the powered Baskakov basis. We prove that in the particular case of squared Baskakov basis the operators behave better than the classical Baskakov operators. For this particular case we give also a quantitative Voronovskaya type result.

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