scholarly journals Asymptotic Formulae via a Korovkin-Type Result

2012 ◽  
Vol 2012 ◽  
pp. 1-12 ◽  
Author(s):  
Daniel Cárdenas-Morales ◽  
Pedro Garrancho ◽  
Ioan Raşa
Keyword(s):  
Positive Operators ◽  
Type Result ◽  
Linear Positive Operators ◽  
Asymptotic Formulae

We present a sort of Korovkin-type result that provides a tool to obtain asymptotic formulae for sequences of linear positive operators.

King type generalization of Baskakov operators based on (𝑝, 𝑞) calculus with better approximation properties

Analysis ◽  
2020 ◽  
Vol 40 (4) ◽  
pp. 163-173
Author(s):  
Lakshmi Narayan Mishra ◽  
Shikha Pandey ◽  
Vishnu Narayan Mishra
Keyword(s):  
Modulus Of Continuity ◽  
Research Area ◽  
Positive Operators ◽  
Order Of Approximation ◽  
Approximation Properties ◽  
Statistical Approximation ◽  
Type Result ◽  
Baskakov Operators ◽  
Linear Positive Operators ◽  
Test Function

AbstractApproximation using linear positive operators is a well-studied research area. Many operators and their generalizations are investigated for their better approximation properties. In the present paper, we construct and investigate a variant of modified (p,q)-Baskakov operators, which reproduce the test function x^{2}. We have determined the order of approximation of the operators via K-functional and second order, the usual modulus of continuity, weighted and statistical approximation properties. In the end, some graphical results which depict the comparison with (p,q)-Baskakov operators are explained and a Voronovskaja type result is obtained.

On the approximation of convex functions using linear positive operators

2017 ◽  
Vol 26 (2) ◽  
pp. 137-143
Author(s):  
DAN BARBOSU
Keyword(s):  
Convex Functions ◽  
Remainder Term ◽  
Mean Value ◽  
Positive Operators ◽  
Linear Functionals ◽  
Linear Positive Operators ◽  
Famous Theorem ◽  
Approximation Formulas ◽  
Phd Thesis ◽  
Higher Order Convexity

The goal of the paper is to present some results concerning the approximation of convex functions by linear positive operators. First, one recalls some results concerning the univariate real valued convex functions. Next, one presents the notion of higher order convexity introduced by Popoviciu [Popoviciu, T., Sur quelques propri´et´ees des fonctions d’une ou deux variable r´eelles, PhD Thesis, La Faculte des Sciences de Paris, 1933 (June)] . The Popoviciu’s famous theorem for the representation of linear functionals associated to convex functions of m−th order (with the proof of author) is also presented. Finally, applications of the convexity to study the monotonicity of sequences of some linear positive operators and also mean value theorems for the remainder term of some approximation formulas based on linear positive operators are presented.

Inverse theorems for some linear positive operators using Beta and Baskakov basis functions

2021 ◽  
Author(s):  
Lakshmi Narayan Mishra ◽  
A. Srivastava ◽  
T. Khan ◽  
S. A. Khan ◽  
Vishnu Narayan Mishra
Keyword(s):  
Positive Operators ◽  
Basis Functions ◽  
Linear Positive Operators ◽  
Inverse Theorems

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 TheΘ-transformation of certain positive linear operators

1996 ◽  
Vol 19 (4) ◽  
pp. 667-678 ◽  
Author(s):  
Aleandru Lupaş ◽  
Detlef H. Mache
Keyword(s):  
Construction Method ◽  
Positive Operators ◽  
Linear Operators ◽  
Positive Linear Operators ◽  
Order Of Approximation ◽  
Linear Positive Operators

The intention of this paper is to describe a construction method for a new sequence of linear positive operators, which enables us to get a pointwise order of approximation regarding the polynomial summator operators which have “best” properties of approximation.

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