The Approximation of The Continuous Functions by Means of Some Linear Positive Operators

1996 ◽  
Vol 30 (1-2) ◽  
pp. 55-66 ◽  
Author(s):  
Ioan Gavrea
Keyword(s):  
Continuous Functions ◽  
Positive Operators ◽  
Linear Positive Operators

A class of linear positive operators in weighted spaces

2012 ◽  
Vol 62 (1) ◽  
Author(s):  
Ayşegül Erençin ◽  
H. Gül İnce ◽  
Ali Olgun
Keyword(s):  
Differential Equation ◽  
Continuous Functions ◽  
Positive Operators ◽  
Weighted Spaces ◽  
Convergence Properties ◽  
Linear Positive Operators ◽  
Spaces Of Continuous Functions

AbstractIn this paper, we introduce a class of linear positive operators based on q-integers. For these operators we give some convergence properties in weighted spaces of continuous functions and present an application to differential equation related to q-derivatives. Furthermore, we give a Stancu-type remainder.

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
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