scholarly journals Approximation with certain genuine hybrid operators

Filomat ◽  
2018 ◽  
Vol 32 (6) ◽  
pp. 2335-2348
Author(s):  
Vijay Gupta ◽  
Th.M. Rassias ◽  
P.N. Agrawal ◽  
Meenu Goyal
Keyword(s):  
Asymptotic Formula ◽  
Present Article ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Integral Type ◽  
General Sequence ◽  
First Order ◽  
Error Estimations ◽  
Direct Results

In the present article, we introduce a general sequence of summation-integral type operators. We establish some direct results which include Voronovskaja type asymptotic formula, point-wise convergence for derivatives, error estimations in terms of modulus of continuity and weighted approximation for these operators. Furthermore, the convergence of these operators and their first order derivatives to certain functions and their corresponding derivatives respectively is illustrated by graphics using Matlab algorithms for some particular values of the parameters c and ?.

scholarly journals Approximation Properties of Certain Summation Integral Type Operators

2015 ◽  
Vol 48 (1) ◽  
Author(s):  
P. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Positive Operators ◽  
Inverse Theorem ◽  
Approximation Properties ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Direct Results

AbstractIn the present paper, we study approximation properties of a family of linear positive operators and establish direct results, asymptotic formula, rate of convergence, weighted approximation theorem, inverse theorem and better approximation for this family of linear positive operators.

scholarly journals New modified Baskakov operators based on the inverse Pólya-Eggenberger distribution

Filomat ◽  
2019 ◽  
Vol 33 (11) ◽  
pp. 3537-3550
Author(s):  
Naokant Deo ◽  
Minakshi Dhamija ◽  
Dan Miclăuş
Keyword(s):  
Asymptotic Formula ◽  
Uniform Convergence ◽  
Present Article ◽  
Baskakov Operators ◽  
Direct Results

In the present article we introduce some modifications of the Baskakov operators in sense of the Lupa? operators based on the inverse P?lya-Eggenberger distribution. For these new modifications we derive some direct results concerning the uniform convergence and the asymptotic formula, as well as some quantitative type theorems.

scholarly journals Approximation Properties of New Modified Gamma Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Yun-Shun Wu ◽  
Wen-Tao Cheng ◽  
Wei-Ping Zhou ◽  
Lun-Zhi Deng
Keyword(s):  
Asymptotic Formula ◽  
Weighted Approximation ◽  
Central Moment ◽  
Sixth Order ◽  
Approximation Properties ◽  
Central Moments ◽  
Type Approximation ◽  
Quantitative Properties ◽  
The Moment ◽  
Direct Results

This paper is aimed at constructing new modified Gamma operators using the second central moment of the classic Gamma operators. And we will compute the first, second, fourth, and sixth order central moments by the moment computation formulas, and their quantitative properties are researched. Then, the global results are established in certain weighted spaces and the direct results including the Voronovskaya-type asymptotic formula, and point-wise estimates are investigated. Also, weighted approximation of these operators is discussed. Finally, the quantitative Voronovskaya-type asymptotic formula and Grüss Voronovskaya-type approximation are presented.

scholarly journals On (p,q)-Analogue of Gamma Operators

2019 ◽  
Vol 2019 ◽  
pp. 1-6 ◽  
Author(s):  
Wen-Tao Cheng ◽  
Wen-Hui Zhang
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation

In this paper, a kind of new analogue of Gamma type operators based on (p,q)-integers is introduced. The Voronovskaja type asymptotic formula of these operators is investigated. And some other results of these operators are studied by means of modulus of continuity and Peetre K-functional. Finally, some direct theorems concerned with the rate of convergence and the weighted approximation for these operators are also obtained.

Genuine link Baskakov–Durrmeyer operators

2018 ◽  
Vol 25 (1) ◽  
pp. 25-40 ◽  
Author(s):  
Vijay Gupta ◽  
Neha Malik
Keyword(s):  
Asymptotic Formula ◽  
Simultaneous Approximation ◽  
Weighted Approximation ◽  
Approximation Result ◽  
Durrmeyer Operators ◽  
Direct Results

AbstractIn the present paper, we propose a sequence of generalized genuine Baskakov–Durrmeyer-type link operators. In terms of ordinary approximation, we estimate local and global direct results and also study the weighted approximation result. In terms of simultaneous approximation, we establish an asymptotic formula of Voronovskaja kind. In the last section, we prove convergence in{L_{p}}-norm.

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 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 Direct estimations of new generalized Baskakov-Szász operators

2016 ◽  
Vol 99 (113) ◽  
pp. 265-279 ◽  
Author(s):  
Vijay Gupta ◽  
Neha Malik
Keyword(s):  
Asymptotic Formula ◽  
Modulus Of Continuity ◽  
Direct Result ◽  
Integral Type ◽  
Szász Operators ◽  
Convergence Results ◽  
Discrete Operators ◽  
Special Case

Several modifications of the discrete operators are available in the literature. In the recent years, certain modifications of the well-known Baskakov and Szasz-Mirakyan operators have been discussed based on certain parameters. We propose mixed summation-integral type operators and estimate the quantitative asymptotic formula and a global direct result for the special case. For general case, we establish moments and some direct convergence results in ordinary approximation, which includes point wise approximation, asymptotic formula and a direct result in terms of modulus of continuity.

Some approximation properties of a kind of (p, q)-Phillips operators

2019 ◽  
Vol 69 (6) ◽  
pp. 1381-1394
Author(s):  
Wentao Cheng ◽  
Chunyan Gui ◽  
Yongmo Hu
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Modulus Of Continuity ◽  
Weighted Approximation ◽  
Local Approximation ◽  
Approximation Properties ◽  
Phillips Operators

Abstract In this paper, a kind of new analogue of Phillips operators based on (p, q)-integers is introduced. The moments of the operators are established. Then some local approximation for the above operators is discussed. Also, the rate of convergence and weighted approximation by these operators by means of modulus of continuity are studied. Furthermore, the Voronovskaja type asymptotic formula is investigated.

scholarly journals Approximation by generalized Srivastava-Gupta operators based on certain parameter

2017 ◽  
Vol 101 (115) ◽  
pp. 247-259 ◽  
Author(s):  
D.K. Verma
Keyword(s):  
Asymptotic Formula ◽  
Error Estimate ◽  
Modulus Of Continuity ◽  
Pointwise Convergence ◽  
Simultaneous Approximation ◽  
Direct Results

We establish some direct results in simultaneous approximation for a generalization of the Srivastava-Gupta operators. We establish pointwise convergence, Voronovskaja type asymptotic formula and an error estimate in terms of modulus of continuity of the function.

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