Quantitative approximation by Stancu-Durrmeyer-Choquet-Šipoš operators

2019 ◽  
Vol 69 (3) ◽  
pp. 625-638
Author(s):  
Sorin G. Gal
Keyword(s):  
Modulus Of Continuity ◽  
Dimensional Simplex ◽  
Set Functions ◽  
Quantitative Estimates ◽  
Choquet Integrals

Abstract In this paper we present general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Stancu-Durrmeyer-Choquet-Šipoš operators $\begin{array}{} M_{n, \Gamma_{n, x}}^{(\beta, \gamma)} \end{array} $, with 0 ≤ β ≤ γ, written in terms of Choquet and Šipoš integrals with respect to a family of monotone and submodular set functions, Γn, x, on the standard d-dimensional simplex. If d = 1 and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.

scholarly journals Quantitative estimates in uniform and pointwise approximation by Bernstein-Durrmeyer-Choquet operators

2017 ◽  
Vol 33 (1) ◽  
pp. 49-58
Author(s):  
SORIN G. GAL ◽  
◽  
SORIN TRIFA ◽  
Keyword(s):  
Modulus Of Continuity ◽  
Pointwise Approximation ◽  
Dimensional Simplex ◽  
Set Functions ◽  
Quantitative Estimates ◽  
Durrmeyer Operator ◽  
Choquet Integrals

For the qualitative results of uniform and pointwise approximation obtained in [8], we present here general quantitative estimates in terms of the modulus of continuity and of a K-functional, in approximation by the generalized multivariate Bernstein-Durrmeyer operator Mn,Γn,x, written in terms of Choquet integrals with respect to a family of monotone and submodular set functions, Γn,x, on the standard d-dimensional simplex. If d = 1 and the Choquet integrals are taken with respect to some concrete possibility measures, the estimate in terms of the modulus of continuity is detailed. Examples improving the estimates given by the classical operators also are presented.

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.

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 Quantitative estimates for Szász operators and its hybrid variant

Filomat ◽  
2021 ◽  
Vol 35 (4) ◽  
pp. 1107-1114
Author(s):  
Ekta Pandey
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Approximation Properties ◽  
Weighted Modulus Of Continuity ◽  
Baskakov Operators ◽  
Szász Operators ◽  
Quantitative Estimates ◽  
Weighted Modulus

The present article deals with the study on approximation properties of well known Sz?sz-Mirakyan operators. We estimate the quantitative Voronovskaja type asymptotic formula for the Sz?sz-Baskakov operators and difference between Sz?sz-Mirakyan operators and the hybrid Sz?sz operators having weights of Baskakov basis in terms of the weighted modulus of continuity

scholarly journals Quantitative estimates for the tensor product (p,q)-Balázs-Szabados operators and associated generalized Boolean sum operators

Filomat ◽  
2020 ◽  
Vol 34 (3) ◽  
pp. 779-793
Author(s):  
Esma Özkan
Keyword(s):  
Tensor Product ◽  
Modulus Of Continuity ◽  
Continuous Functions ◽  
Modulus Of Smoothness ◽  
Mixed Modulus Of Smoothness ◽  
Quantitative Estimates ◽  
Gbs Operators ◽  
Mixed Modulus ◽  
Boolean Sum ◽  
Second Modulus Of Continuity

In this study, we give some approximation results for the tensor product of (p,q)-Bal?zs-Szabados operators associated generalized Boolean sum (GBS) operators. Firstly, we introduce tensor product (p,q)-Bal?zs-Szabados operators and give an uniform convergence theorem of these operators on compact rectangular regions with an illustrative example. Then we estimate the approximation for the tensor product (p,q)-Bal?zs-Szabados operators in terms of the complete modulus of continuity, the partial modulus of continuity, Lipschitz functions and Petree?s K-functional corresponding to the second modulus of continuity. After that, we introduce the GBS operators associated the tensor product (p,q)-Bal?zs-Szabados operators. Finally, we improve the rate of smoothness by the mixed modulus of smoothness and Lipschitz class of B?gel continuous functions for the GBS operators.

scholarly journals Quantitative approximation by nonlinear convolution operators of Landau-Choquet type

2020 ◽  
Vol 36 (3) ◽  
pp. 415-422
Author(s):  
SORIN G. GAL ◽  
IONUT T. IANCU
Keyword(s):  
Modulus Of Continuity ◽  
Convolution Operators ◽  
Approximation Properties ◽  
Set Functions ◽  
Monotone Set Function ◽  
Set Function

By using the concept of Choquet nonlinear integral with respect to a monotone set function, we introduce the nonlinear convolution operators of Landau-Choquet type, with respect to a family of submodular set functions. Quantitative approximation results in terms of the modulus of continuity are obtained with respect to some particular possibility measures. For some subclasses of functions we prove that these Landau-Choquet type operators can have essentially better approximation properties than their classical correspondents.

Durrmeyer type modification of (p,q)-Szász Mirakjan operators and their quantitative estimates

2021 ◽  
Vol 30 (1) ◽  
pp. 97-106
Author(s):  
HONEY SHARMA ◽  
RAMAPATI MAURYA
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Local Approximation ◽  
Quantitative Estimates ◽  
Kantorovich Operators ◽  
Oper Ators

In the present paper, we introduce Durrmeyer type modification of (p, q)-Szasz Mirakjan oper- ´ ators. We estimate the rate of convergence and local approximation behavior of the operators using modulus of continuity and Peetre’s K-functional. We compute the quantitative estimates for difference of the proposed operators with (p, q)-Szasz Mirakjan operators and ´ (p, q)-Szasz Mirakjan Kantorovich operators.

scholarly journals Sharp estimates of approximation by some positive linear operators

1984 ◽  
Vol 29 (1) ◽  
pp. 13-18 ◽  
Author(s):  
Ashok Sahai ◽  
Govind Prasad
Keyword(s):  
Modulus Of Continuity ◽  
Bernstein Polynomials ◽  
Higher Order ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Higher Order Moments ◽  
Sharp Estimates ◽  
Quantitative Estimates ◽  
Image Position

Recently, Varshney and Singh [Rend. Mat. (6) 2 (1982), 219–225] have given sharper quantitative estimates of convergence for Bernstein polynomials, Szasz and Meyer-Konig-Zeller operators. We have achieved improvement over these estimates by taking moments of higher order. For example, in case of the Meyer-Konig-Zeller operator, they gave the following estimatewherein ∥·∥ stands for sup norm. We have improved this result toWe may remark here that for this modulus of continuity ) our result cannot be sharpened further by taking higher order moments.

Sign in / Sign up

Export Citation Format

Share Document