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 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 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 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 of New Sequence of Integral Type Operators with two Parameters

2020 ◽  
Vol 19 ◽  
pp. 89-95
Author(s):  
Amal Khaleel ◽  
Amal K. Hassan
Keyword(s):  
Asymptotic Formula ◽  
Error Estimates ◽  
Modulus Of Continuity ◽  
Linear Operators ◽  
Integral Type ◽  
Numerical Example ◽  
Two Parameters ◽  
Positive Integers

In our paper, we provide and study a new sequence of positive and linear operators of integral type. This sequence depends on two parameters, positive integers and. We mention some of the properties of this sequence and describe a Voronovskaja type asymptotic formula. Besides, we find the error estimates of this approximation in terms of the modulus of continuity. lastly, we introduce a numerical example and compare the results obtained.

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. 

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.

An Application of Separate Convergence for Continued Fractions to Orthogonal Polynomials

1992 ◽  
Vol 35 (3) ◽  
pp. 381-389
Author(s):  
William B. Jones ◽  
W. J. Thron ◽  
Nancy J. Wyshinski
Keyword(s):  
Distribution Function ◽  
Asymptotic Formula ◽  
Orthogonal Polynomial ◽  
Orthogonal Polynomials ◽  
Continued Fractions ◽  
Polynomial Sequence ◽  
Convergence Results ◽  
Compact Subsets

AbstractIt is known that the n-th denominators Qn (α, β, z) of a real J-fractionwhereform an orthogonal polynomial sequence (OPS) with respect to a distribution function ψ(t) on ℝ. We use separate convergence results for continued fractions to prove the asymptotic formulathe convergence being uniform on compact subsets of

A Risk Model with Delayed Claims

2013 ◽  
Vol 50 (03) ◽  
pp. 686-702 ◽  
Author(s):  
Angelos Dassios ◽  
Hongbiao Zhao
Keyword(s):  
Asymptotic Formula ◽  
Poisson Process ◽  
Ruin Probability ◽  
Risk Model ◽  
Poisson Model ◽  
Exact Formula ◽  
Poisson Models ◽  
Asymptotic Expressions ◽  
Special Case

In this paper we introduce a simple risk model with delayed claims, an extension of the classical Poisson model. The claims are assumed to arrive according to a Poisson process and claims follow a light-tailed distribution, and each loss payment of the claims will be settled with a random period of delay. We obtain asymptotic expressions for the ruin probability by exploiting a connection to Poisson models that are not time homogeneous. A finer asymptotic formula is obtained for the special case of exponentially delayed claims and an exact formula is obtained when the claims are also exponentially distributed.

scholarly journals Dunkl Generalization of Phillips Operators and Approximation in Weighted Spaces

2020 ◽  
Author(s):  
M. Mursaleen ◽  
Md Nasiruzzaman ◽  
Adem Kilicman ◽  
Siti Hasana Sapar
Keyword(s):  
Rate Of Convergence ◽  
Error Estimation ◽  
Modulus Of Continuity ◽  
Second Order ◽  
Maximal Functions ◽  
Weighted Spaces ◽  
Phillips Operators ◽  
Convergence Results

Purpose of this article is to introduce a modification of Phillips operators on the interval $\left[ \frac{1}{2},\infty \right) $ via Dunkl generalization. This type of modification enables a better error estimation on the interval $\left[ \frac{1}{2},\infty \right) $ rather than the classical Dunkl Phillips operators on $\left[ 0,\infty \right) $. We discuss the convergence results and obtain the degrees of approximations. Furthermore, we calculate the rate of convergence by means of modulus of continuity, Lipschitz type maximal functions, Peetre's $K$-functional and second order modulus of continuity.

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