scholarly journals Approximation by Bézier Variant of Baskakov-Durrmeyer-Type Hybrid Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Lahsen Aharouch ◽  
Khursheed J. Ansari ◽  
M. Mursaleen
Keyword(s):  
Rate Of Convergence ◽  
Present Article ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Lipschitz Function ◽  
Modulus Of Smoothness ◽  
Weighted Modulus Of Continuity ◽  
Type Formula ◽  
Weighted Modulus ◽  
Bézier Variant

We give a Bézier variant of Baskakov-Durrmeyer-type hybrid operators in the present article. First, we obtain the rate of convergence by using Ditzian-Totik modulus of smoothness and also for a class of Lipschitz function. Then, weighted modulus of continuity is investigated too. We study the rate of point-wise convergence for the functions having a derivative of bounded variation. Furthermore, we establish the quantitative Voronovskaja-type formula in terms of Ditzian-Totik modulus of smoothness at the end.

scholarly journals Rate of convergence of Szász-beta operators based on q-integers

2017 ◽  
Vol 50 (1) ◽  
pp. 130-143 ◽  
Author(s):  
Pooja Gupta ◽  
Purshottam Narain Agrawal
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Maximal Function ◽  
Statistical Convergence ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus ◽  
Lipschitz Type Maximal Function

Abstract The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

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 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 Bézier variant of the Szász-Durrmeyer type operators based on the Poisson-Charlier polynomials

Filomat ◽  
2020 ◽  
Vol 34 (10) ◽  
pp. 3265-3273
Author(s):  
Arun Kajla ◽  
Dan Miclăuş
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Charlier Polynomials ◽  
Durrmeyer Type Operators ◽  
Direct Approximation ◽  
Bézier Variant

In the present paper we introduce the B?zier variant of the Sz?sz-Durrmeyer type operators, involving the Poisson-Charlier polynomials. Our study focuses on a direct approximation theorem in terms of the Ditzian-Totik modulus of smoothness and the rate of convergence for differential functions whose derivatives are of bounded variation.

scholarly journals Approximation by generalized Stancu type integral operators involving Sheffer polynomials

2018 ◽  
Vol 34 (2) ◽  
pp. 215-228
Author(s):  
M. MURSALEEN ◽  
◽  
SHAGUFTA RAHMAN ◽  
KHURSHEED J. ANSARI ◽  
◽  
...  
Keyword(s):  
Modulus Of Continuity ◽  
Integral Operators ◽  
Modulus Of Smoothness ◽  
Approximation Properties ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Type Integral ◽  
Weighted Modulus ◽  
Sheffer Polynomials ◽  
Korovkin’S Theorem

In this article, we give a generalization of integral operators which involves Sheffer polynomials introduced by Sucu and Buy¨ ukyazici. We obtain approximation properties of our operators with the help of the univer- ¨ sal Korovkin’s theorem and study convergence properties by using modulus of continuity, the second order modulus of smoothness and Peetre’s K-functional. We have also established Voronovskaja type asymptotic formula. Furthermore, we study the convergence of these operators in weighted spaces of functions on the positive semi-axis and estimate the approximation by using weighted modulus of continuity.

scholarly journals Approximation by Szász-Jakimovski-Leviatan-Type Operators via Aid of Appell Polynomials

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Md. Nasiruzzaman ◽  
A. F. Aljohani
Keyword(s):  
Present Article ◽  
Modulus Of Continuity ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Approximation Properties ◽  
Appell Polynomials ◽  
Weighted Modulus Of Continuity ◽  
Dunkl Analogue ◽  
Weighted Modulus ◽  
Convergence Of Operators

The main purpose of the present article is to construct a newly Szász-Jakimovski-Leviatan-type positive linear operators in the Dunkl analogue by the aid of Appell polynomials. In order to investigate the approximation properties of these operators, first we estimate the moments and obtain the basic results. Further, we study the approximation by the use of modulus of continuity in the spaces of the Lipschitz functions, Peetres K-functional, and weighted modulus of continuity. Moreover, we study A-statistical convergence of operators and approximation properties of the bivariate case.

Dunkl generalization of Kantorovich type Szász–Mirakjan operators via q-calculus

2017 ◽  
Vol 10 (04) ◽  
pp. 1750077 ◽  
Author(s):  
M. Mursaleen ◽  
Md. Nasiruzzaman
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Exponential Function ◽  
Type Theorem ◽  
Second Order ◽  
Convergence Properties ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus

In this paper, we construct Kantorovich type Szász–Mirakjan operators generated by Dunkl generalization of the exponential function via [Formula: see text]-integers. We obtain some approximation results via well-known Korovkin’s type theorem for these operators and study convergence properties by using the modulus of continuity. Furthermore, we obtain the rate of convergence in terms of the classical, second-order, and weighted modulus of continuity.

Bézier variant of Bernstein–Durrmeyer blending-type operators

2021 ◽  
pp. 2250103
Author(s):  
Chandra Prakash ◽  
Naokant Deo ◽  
D. K. Verma
Keyword(s):  
Rate Of Convergence ◽  
Bounded Variation ◽  
Modulus Of Continuity ◽  
Graphical Representation ◽  
Type Function ◽  
Rate Of Approximation ◽  
Durrmeyer Type Operators ◽  
Derivatives Of ◽  
Theoretical Results ◽  
Bézier Variant

In this paper, we construct the Bézier variant of the Bernstein–Durrmeyer-type operators. First, we estimated the moments for these operators. In the next section, we found the rate of approximation of operators [Formula: see text] using the Lipschitz-type function and in terms of Ditzian–Totik modulus of continuity. The rate of convergence for functions having derivatives of bounded variation is discussed. Finally, the graphical representation of the theoretical results and the effectiveness of the defined operators are given.

scholarly journals Approximation by a generalization of Szasz-Mirakjan type operators

2020 ◽  
Vol 65 (4) ◽  
pp. 575-583
Author(s):  
Mohammed Arif Siddiqui ◽  
Nandita Gupta
Keyword(s):  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Asymptotic Estimate ◽  
Type Result ◽  
Weighted Modulus Of Continuity ◽  
Weighted Modulus

In the present paper we propose a new generalization of Sz\'{a}sz-Mirakjan-type operators. We discuss their weighted convergence and rate of convergence via weighted modulus of continuity. We also give an asymptotic estimate through Voronovskaja type result for these operators.

Modified Lupaş-Jain operators

2020 ◽  
Vol 70 (2) ◽  
pp. 431-440 ◽  
Author(s):  
Murat Bodur
Keyword(s):  
Modulus Of Continuity ◽  
Type Theorem ◽  
Weighted Spaces ◽  
Order Of Approximation ◽  
Weighted Modulus Of Continuity ◽  
Quantitative Form ◽  
Voronovskaya Type Theorem ◽  
Weighted Modulus

Abstract The goal of this paper is to propose a modification of Lupaş-Jain operators based on a function ρ having some properties. Primarily, the convergence of given operators in weighted spaces is discussed. Then, order of approximation via weighted modulus of continuity is computed for these operators. Further, Voronovskaya type theorem in quantitative form is taken into consideration, as well. Ultimately, some graphical results that illustrate the convergence of investigated operators to f are given.

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