On the degree of the approximation of functions of several variables by linear positive operators of finite rank

1993 ◽  
Vol 53 (1) ◽  
pp. 3-11 ◽  
Author(s):  
R. K. Vasil'ev
Keyword(s):  
Finite Rank ◽  
Positive Operators ◽  
Approximation Of Functions ◽  
Linear Positive Operators ◽  
Several Variables

scholarly journals Approximation of functions of two variables by certain linear positive operators

2007 ◽  
Vol 117 (3) ◽  
pp. 387-399 ◽  
Author(s):  
Fatma Taşdelen ◽  
Ali Olgun ◽  
Gülen Başcanbaz-Tunca
Keyword(s):  
Positive Operators ◽  
Approximation Of Functions ◽  
Linear Positive Operators ◽  
Functions Of Two Variables

scholarly journals Approximation of functions with linear positive operators which fix {1, φ} and {1, φ2}

2020 ◽  
Vol 28 (3) ◽  
pp. 255-265
Author(s):  
Fuat Usta
Keyword(s):  
Positive Operators ◽  
Approximation Of Functions ◽  
Linear Positive Operators ◽  
Different Types ◽  
Unbounded Intervals

AbstractIn this manuscript, linear and positive operators described on bounded and unbounded intervals that fix the function sets {1, φ} and {1, φ2} such that φ ∈ C[0, 1] are presented. Then we present different types of operators by choosing different functions and values. Finally, Voronovskaya type theorems are given for this newly defined sequences of linear and positive operators.

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.

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