scholarly journals A note on some positive linear operators associated with the Hermite polynomials

2016 ◽  
Vol 32 (1) ◽  
pp. 71-77
Author(s):  
GRAZYNA KRECH ◽  
Keyword(s):  
Asymptotic Formula ◽  
Hermite Polynomials ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Approximation Theorems ◽  
Direct Approximation

In this paper we give direct approximation theorems and the Voronovskaya type asymptotic formula for certain linear operators associated with the Hermite polynomials. These operators extend the well-known Szasz-Mirakjan operators.

scholarly journals Some Approximation Properties of Modified Jain-Beta Operators

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Vishnu Narayan Mishra ◽  
Prashantkumar Patel
Keyword(s):  
Asymptotic Formula ◽  
Rate Of Convergence ◽  
Basis Function ◽  
Function Approximation ◽  
Approximation Theorem ◽  
Weighted Approximation ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Weight Functions ◽  
Approximation Properties

Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters α, β, and γ and discuss Voronovskaja asymptotic formula.

Deferred weighted 𝒜-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems

2018 ◽  
Vol 24 (1) ◽  
pp. 1-16 ◽  
Author(s):  
H. M. Srivastava ◽  
Bidu Bhusan Jena ◽  
Susanta Kumar Paikray ◽  
U. K. Misra
Keyword(s):  
Statistical Convergence ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Statistical Approximation ◽  
Lagrange Polynomials ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Special Cases ◽  
Korovkin Type Approximation Theorems ◽  
Appl Math

AbstractRecently, the notion of positive linear operators by means of basic (orq-) Lagrange polynomials and{\mathcal{A}}-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means ofq-Lagrange polynomials andA-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911–6918]. In our present investigation, we introduce a certain deferred weighted{\mathcal{A}}-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1,tand{t^{2}}defined on a Banach space{C[0,1]}for a sequence of (presumably new) positive linear operators based upon{(p,q)}-Lagrange polynomials. Furthermore, we investigate the deferred weighted{\mathcal{A}}-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

scholarly journals Korovkin Second Theorem via -Statistical -Summability

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
M. Mursaleen ◽  
A. Kiliçman
Keyword(s):  
Continuous Functions ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Real Interval ◽  
Test Functions ◽  
Approximation Process ◽  
The Real ◽  
Approximation Theorems ◽  
Whole Space ◽  
Korovkin Type Approximation Theorems

Korovkin type approximation theorems are useful tools to check whether a given sequence of positive linear operators on of all continuous functions on the real interval is an approximation process. That is, these theorems exhibit a variety of test functions which assure that the approximation property holds on the whole space if it holds for them. Such a property was discovered by Korovkin in 1953 for the functions 1, , and in the space as well as for the functions 1, cos, and sin in the space of all continuous 2-periodic functions on the real line. In this paper, we use the notion of -statistical -summability to prove the Korovkin second approximation theorem. We also study the rate of -statistical -summability of a sequence of positive linear operators defined from into .

scholarly journals An Asymptotic Formula of Modified Family of Positive Linear Operators

10.29007/qcdz ◽  
2018 ◽  
Author(s):  
Prashantkumar Patel ◽  
Vishnu Narayan Mishra
Keyword(s):  
Asymptotic Formula ◽  
Linear Operators ◽  
Positive Linear Operators

In 2016, Patel and Mishra introduce the operators which is generalization of well-known Szasz- Mirakyan operators. In this manuscript, we have discussed Voronovskaja asymptotic of Stancu type generalization of the operators defined by Patel and Mishra.

I-convergence theorems for a class of k-positive linear operators

2009 ◽  
Vol 7 (2) ◽  
Author(s):  
Mehmet Özarslan
Keyword(s):  
Unit Disc ◽  
Statistical Convergence ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Convergence Theorems ◽  
Approximation Theorems ◽  
Analytical Functions

AbstractIn this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

scholarly journals ABSTRACT KOROVKIN THEOREMS VIA RELATIVE MODULAR CONVERGENCE FOR DOUBLE SEQUENCES OF LINEAR OPERATORS

2020 ◽  
pp. 561
Author(s):  
Sevda Yıldız ◽  
Kamil Demirci
Keyword(s):  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Double Sequences ◽  
Approximation Theorems ◽  
Type Approximation ◽  
Modular Spaces ◽  
Abstract Version ◽  
Modular Convergence ◽  
Korovkin Type Approximation Theorems

We will obtain an abstract version of the Korovkin type approximation theorems with respect to the concept of statistical relative convergence in modular spaces for double sequences of positive linear operators. We will give an application showing that our results are stronger than classical ones. We will also study an extension to non-positive operators.

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