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.

scholarly journals Some Approximation Properties for Modified Baskakov Type Operators

2005 ◽  
Vol 12 (2) ◽  
pp. 217-228
Author(s):  
Vijay Gupta
Keyword(s):  
Modulus Of Continuity ◽  
Simultaneous Approximation ◽  
Higher Order ◽  
Approximation Properties ◽  
Linear Combinations ◽  
Steklov Mean ◽  
Estimation Of Error ◽  
Direct Results

Abstract We study some direct results for the recently introduced family of modified Baskakov type operators. In particular, we obtain local direct results on ordinary and simultaneous approximation and an estimation of error for linear combinations in terms of higher order modulus of continuity. We have applied the Steklov mean as a tool for the linear approximating method.

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 On Simultaneous Approximation of Modified Baskakov-Durrmeyer Operators

2015 ◽  
Vol 2015 ◽  
pp. 1-10 ◽  
Author(s):  
Prashantkumar G. Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Error Estimation ◽  
Pointwise Convergence ◽  
Simultaneous Approximation ◽  
Second Order ◽  
Durrmeyer Operators

We discuss properties of modified Baskakov-Durrmeyer-Stancu (BDS) operators with parameter γ>0. We compute the moments of these modified operators. Also, we establish pointwise convergence, Voronovskaja type asymptotic formula, and an error estimation in terms of second order modification of continuity of the function for the operators Bn,γα,β(f,x).

scholarly journals Convergence estimates of a family of approximation operators of exponential type

Filomat ◽  
2020 ◽  
Vol 34 (13) ◽  
pp. 4329-4341
Author(s):  
Vijay Gupta ◽  
Manuel López-Pellicer ◽  
H.M. Srivastava
Keyword(s):  
Asymptotic Formula ◽  
Modulus Of Continuity ◽  
Exponential Type ◽  
Exponential Growth ◽  
Simultaneous Approximation ◽  
Type Result ◽  
Exponential Functions ◽  
Approximation Operators ◽  
Convergence Estimates

The main object of this article is to consider a family of approximation operators of exponential type, which has presumably not been studied earlier due mainly to their seemingly complicated behavior. We estimate and establish a quantitative asymptotic formula in terms of the modulus of continuity with exponential growth, a Korovkin-type result for exponential functions and also a Voronovskaja-type asymptotic formula in the simultaneous approximation.

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 Simultaneous Approximation of New Sequence of Integral Type Operators with Parameter δ_0

2019 ◽  
Vol 12 (4) ◽  
pp. 1508-1523 ◽  
Author(s):  
Ali Jassim Mohammad ◽  
Hadeel Omar Muslim
Keyword(s):  
Asymptotic Formula ◽  
Modulus Of Continuity ◽  
Convergence Theorem ◽  
Simultaneous Approximation ◽  
Test Functions ◽  
Integral Type ◽  
Linear Positive Operators ◽  
Numerical Examples ◽  
Szász Operators ◽  
Better Than

In this paper, we define a new sequence of linear positive operators of integral type to approximate functions in the space,. First, we study the basic convergence theorem in simultaneous approximation and then study Voronovskaja-type asymptotic formula. Then, we estimate an error occurs by this approximation in the terms of the modulus of continuity. Next, we give numerical examples to approximate three test functions in the space by the sequence. Finally, we compare the results with the classical sequence of Szãsz operators  on the interval . It turns out that, the sequence  gives better than the results of the sequence  for the two test functions using in the numerical examples.

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 Simultaneous Approximation by a New Sequence of Integral Type Based on Two Parameters

2021 ◽  
pp. 1666-1674
Author(s):  
Ali J. Mohammad ◽  
Amal K. Hassan
Keyword(s):  
Asymptotic Formula ◽  
Simultaneous Approximation ◽  
Linear Operators ◽  
Order Of Approximation ◽  
Integral Type ◽  
Test Function ◽  
Numerical Example ◽  
First Derivative ◽  
Two Parameters

This paper introduces a generalization sequence of positive and linear operators of integral type based on two parameters to improve the order of approximation. First, the simultaneous approximation is studied and a Voronovskaja-type asymptotic formula is introduced. Next, an error of the estimation in the simultaneous approximation is found. Finally, a numerical example to approximate a test function and its first derivative of this function is given for some values of the parameters. 

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 On Approximation by Gupta type general family of Operators

2021 ◽  
Author(s):  
Karunesh Singh
Keyword(s):  
Modulus Of Continuity ◽  
Approximation Theorem ◽  
Modulus Of Smoothness ◽  
Linear Operators ◽  
Asymptotic Result ◽  
Linear Positive Operators ◽  
Type Approximation ◽  
Quantitative Form ◽  
Wide Range ◽  
Direct Results

In this paper, we study Gupta type family of positive linear operators, which have a wide range of many well known linear positive operators e.g. Phillips, Baskakov-Durrmeyer, Baskakov-Sz\’{a}sz, Sz\’{a}sz-Beta, Lupa\c{s}-Beta, Lupa\c{s}-Sz\’{a}sz, genuine Bernstein-Durrmeyer, Link, P\u{a}lt\u{a}nea, Mihe\c{s}an-Durrmeyer, link Bernstein-Durrmeyer etc. We first establish direct results in terms of usual modulus of continuity having order 2 and Ditzian-Totik modulus of smoothness and then study quantitative Voronovkaya theorem for the weighted spaces of functions. Further, we establish Gr\“{u}ss-Voronovskaja type approximation theorem and also derive Gr\”{u}ss-Voronovskaja type asymptotic result in quantitative form.

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