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 Approximation of General Form for a Sequence of Linear Positive Operators Based on Four Parameters

2018 ◽  
Vol 14 (2) ◽  
pp. 7921-7936
Author(s):  
Khalid Dhaman Abbod ◽  
Ali J. Mohammad
Keyword(s):  
Asymptotic Formula ◽  
Weight Function ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Simultaneous Approximation ◽  
Positive Operators ◽  
Order Moment ◽  
Linear Positive Operators ◽  
Numerical Examples

In the present paper, we define a generalization sequence of linear positive operators based on four parameters which is reduce to many other sequences of summation–integral older type operators of any weight function (Bernstein, Baskakov, Szász or Beta). Firstly, we find a recurrence relation of the -th order moment and study the convergence theorem for this generalization sequence. Secondly, we give a Voronovaskaja-type asymptotic formula for simultaneous approximation. Finally, we introduce some numerical examples to view the effect of the four parameters of this sequence.

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 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.

scholarly journals Approximation properties For generalized S–Szasz Operators with Application

2020 ◽  
Vol 19 ◽  
pp. 47-57
Author(s):  
Khalid D. Abbood
Keyword(s):  
Asymptotic Formula ◽  
Recurrence Relation ◽  
Convergence Theorem ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Order Moment ◽  
Approximation Properties ◽  
Integral Type ◽  
Szász Operators ◽  
Direct Results

This work focuses on a class of positive linear operators of S–Szasz type; we establish some direct results, which include Voronovskaja type asymptotic formula for a sequence of summation–integral type, we find a recurrence relation of the -the order moment and the convergence theorem for this sequence. Finally, we give some figures.

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. 

scholarly journals On Some Extensions of Szasz Operators Including Boas-Buck-Type Polynomials

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Sezgin Sucu ◽  
Gürhan İçöz ◽  
Serhan Varma
Keyword(s):  
Convergence Theorem ◽  
Quantitative Estimation ◽  
Laguerre Polynomials ◽  
Classical Approach ◽  
Type Result ◽  
Linear Positive Operators ◽  
Approximation Process ◽  
Charlier Polynomials ◽  
Szász Operators ◽  
Second Modulus Of Continuity

This paper is concerned with a new sequence of linear positive operators which generalize Szasz operators including Boas-Buck-type polynomials. We establish a convergence theorem for these operators and give the quantitative estimation of the approximation process by using a classical approach and the second modulus of continuity. Some explicit examples of our operators involving Laguerre polynomials, Charlier polynomials, and Gould-Hopper polynomials are given. Moreover, a Voronovskaya-type result is obtained for the operators containing Gould-Hopper polynomials.

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 Convergence of the GAOR Method for One Subclass ofH-Matrix

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Guangbin Wang ◽  
Ting Wang
Keyword(s):  
Linear System ◽  
Convergence Theorem ◽  
Coefficient Matrix ◽  
Linear Least Squares ◽  
Numerical Examples ◽  
Linear Least Squares Problem ◽  
Diagonally Dominant Matrix ◽  
Diagonally Dominant ◽  
Dominant Matrix ◽  
Better Than

We discuss the convergence of the GAOR method to solve linear system which occurred in solving the weighted linear least squares problem. Moreover, we present one convergence theorem of the GAOR method when the coefficient matrix is a strictly doublyαdiagonally dominant matrix which is a nonsingularH-matrix. Finally, we show that our results are better than previous ones by using four numerical examples.

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 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

Sign in / Sign up

Export Citation Format

Share Document