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.

Approximation by max-product sampling Kantorovich operators with generalized kernels

2019 ◽  
pp. 1-26 ◽  
Author(s):  
Lucian Coroianu ◽  
Danilo Costarelli ◽  
Sorin G. Gal ◽  
Gianluca Vinti
Keyword(s):  
Uniform Convergence ◽  
Real Axis ◽  
Modulus Of Continuity ◽  
Higher Dimensions ◽  
Jackson Type ◽  
Convergence Properties ◽  
Type Estimate ◽  
Quantitative Estimates ◽  
Uniform Modulus Of Continuity ◽  
Kantorovich Operators

In a recent paper, for max-product sampling operators based on general kernels with bounded generalized absolute moments, we have obtained several pointwise and uniform convergence properties on bounded intervals or on the whole real axis, including a Jackson-type estimate in terms of the first uniform modulus of continuity. In this paper, first, we prove that for the Kantorovich variants of these max-product sampling operators, under the same assumptions on the kernels, these convergence properties remain valid. Here, we also establish the [Formula: see text] convergence, and quantitative estimates with respect to the [Formula: see text] norm, [Formula: see text]-functionals and [Formula: see text]-modulus of continuity as well. The results are tested on several examples of kernels and possible extensions to higher dimensions are suggested.

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 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 Convergence properties of generalized Lupaş-Kantorovich operators

2021 ◽  
Vol 13 (3) ◽  
pp. 818-830
Author(s):  
M. Qasim ◽  
A. Khan ◽  
Z. Abbas ◽  
M. Mursaleen
Keyword(s):  
Type Theorem ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Convergence Properties ◽  
Unbounded Function ◽  
Quantitative Estimates ◽  
Voronovskaya Type Theorem ◽  
Lupaş Operators ◽  
Kantorovich Operators

In the present paper, we consider the Kantorovich modification of generalized Lupaş operators, whose construction depends on a continuously differentiable, increasing and unbounded function $\rho$. For these new operators we give weighted approximation, Voronovskaya type theorem, quantitative estimates for the local approximation.

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.

Approximation by bivariate (p,q)-Baskakov–Kantorovich operators

2018 ◽  
Vol 25 (3) ◽  
pp. 397-407 ◽  
Author(s):  
Hatice Gul Ince Ilarslan ◽  
Tuncer Acar
Keyword(s):  
Uniform Convergence ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Korovkin Theorem ◽  
Central Moments ◽  
The Korovkin Theorem ◽  
Kantorovich Operators

AbstractThe present paper deals with the bivariate{(p,q)}-Baskakov–Kantorovich operators and their approximation properties. First we construct the operators and obtain some auxiliary results such as calculations of moments and central moments, etc. Our main results consist of uniform convergence of the operators via the Korovkin theorem and rate of convergence in terms of modulus of continuity.

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 Convergence properties of Ibragimov-Gadjiev-Durrmeyer operators

2015 ◽  
Vol 24 (1) ◽  
pp. 17-26
Author(s):  
EMRE DENIZ ◽  
◽  
ALI ARAL ◽  
Keyword(s):  
Weighted Space ◽  
Type Theorem ◽  
Approximation Error ◽  
Weighted Norm ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Korovkin Type Theorem ◽  
Durrmeyer Operators ◽  
Weighted Modulus ◽  
Direct Approximation

The purpose of the present paper is to study the local and global direct approximation properties of the Durrmeyer type generalization of Ibragimov Gadjiev operators defined in [Aral, A. and Acar, T., On Approximation Properties of Generalized Durrmeyer Operators, (submitted)]. The results obtained in this study consist of Korovkin type theorem which enables us to approximate a function uniformly by new Durrmeyer operators, and estimate for approximation error of the operators in terms of weighted modulus of continuity. These results are obtained for the functions which belong to weighted space with polynomial weighted norm by new operators which act on functions defined on the non compact interval [0.∞). We finally present a direct approximation result.

scholarly journals Approximation properties of the new type generalized Bernstein-Kantorovich operators

2021 ◽  
Vol 7 (3) ◽  
pp. 3826-3844
Author(s):  
Mustafa Kara ◽  
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Type Theorem ◽  
Numerical Results ◽  
Bernstein Operators ◽  
Approximation Properties ◽  
Voronovskaya Type Theorem ◽  
New Type ◽  
Kantorovich Operators

<abstract><p>In this paper, we introduce new type of generalized Kantorovich variant of $ \alpha $-Bernstein operators and study their approximation properties. We obtain estimates of rate of convergence involving first and second order modulus of continuity and Lipschitz function are studied for these operators. Furthermore, we establish Voronovskaya type theorem of these operators. The last section is devoted to bivariate new type $ \alpha $-Bernstein-Kantorovich operators and their approximation behaviors. Also, some graphical illustrations and numerical results are provided.</p></abstract>

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).

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