Ioan Raşa
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View article: Positive Linear Operators and Entropies
Positive Linear Operators and Entropies Open
The study of positive linear operators is closely linked to the study of probability distributions. In this paper, we investigate the relationship between classical positive linear operators, commonly used in Approximation Theory, and the …
View article: Asymptotic Properties for a General Class of Szász–Mirakjan–Durrmeyer Operators
Asymptotic Properties for a General Class of Szász–Mirakjan–Durrmeyer Operators Open
In this paper, we introduce a general family of Szász–Mirakjan–Durrmeyer type operators depending on an integer parameter . They can be viewed as a generalization of the Szász–Mirakjan–Durrmeyer operators, Phillips operators, and correspon…
View article: Kernels for composition of positive linear operators
Kernels for composition of positive linear operators Open
This paper investigates the composition of Bernstein--Durrmeyer operators and Szász--Mirakjan--Durrmeyer operators, focusing on the structure and properties of the associated kernel functions. In the case of the Bernstein--Durrmeyer operat…
View article: On Some Cauchy Problems and Positive Linear Operators
On Some Cauchy Problems and Positive Linear Operators Open
Durrmeyer type modifications of the Szász–Mirakjan operators were studied in several papers. We consider a general family of such operators. Basically, we investigate the relationship between the images of a function f under the operators …
View article: Commutativity and spectral properties for a general class of Szász–Mirakjan–Durrmeyer operators
Commutativity and spectral properties for a general class of Szász–Mirakjan–Durrmeyer operators Open
In this paper we present commutativity results for a general class of Szász–Mirakjan–Durrmeyer type operators and associated differential operators and investigate their eigenfunctions.
View article: Commutativity and spectral properties for a general class of Szasz-Mirakjan-Durrmeyer operators
Commutativity and spectral properties for a general class of Szasz-Mirakjan-Durrmeyer operators Open
In this paper we present commutativity results for a general class of Szasz-Mirakjan-Durrmeyer type operators and associated differential operators and investigate their eigenfunctions.
View article: Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators
Asymptotic properties for a general class of Szasz-Mirakjan-Durrmeyer operators Open
In this paper we introduce a general family of Szász--Mirakjan--Durrmeyer type operators depending on an integer parameter $j \in \mathbb{Z}$. They can be viewed as a generalization of the Szász--Mirakjan--Durrmeyer operators [9], Phillips…
View article: Bernstein–Kantorovich operators, approximation and shape preserving properties
Bernstein–Kantorovich operators, approximation and shape preserving properties Open
Inspired by the construction of Bernstein and Kantorovich operators, we introduce a family of positive linear operators $$\mathcal{K}_n$$ preserving the affine functions. Their approximation properties are investigated and compared wit…
View article: Steklov Type Operators and Functional Equations
Steklov Type Operators and Functional Equations Open
We consider sequences of Steklov type operators and an associated functional equation. For a suitable sequence, we establish asymptotic formulas.
View article: Composition of some positive linear integral operators
Composition of some positive linear integral operators Open
This article is devoted to constructing sequences of integral operators with the same Voronovskaja formula as the generalized Baskakov operators, but having different behavior in other respects. For them, we investigate the eigenstructure,…
View article: Bernstein polynomials and dual functionals
Bernstein polynomials and dual functionals Open
The divided differences of Bernstein polynomials were investigated by Alexandru Lupas in 1995. We extend the results of that investigation. Moreover, we establish new relations between them and the theory of dual functionals.
View article: Perov's theorem applied to systems of equations
Perov's theorem applied to systems of equations Open
In this paper, we consider systems of equations having a linear part and also a nonlinear part. We give sufficient conditions which imply the existence and uniqueness of solutions to the system. Using Perov's theorem, our results extend so…
View article: Composition and Decomposition of Positive Linear Operators (VIII)
Composition and Decomposition of Positive Linear Operators (VIII) Open
In a series of papers, most of them authored or co-authored by H. Gonska, several authors investigated problems concerning the composition and decomposition of positive linear operators defined on spaces of functions. For example, given tw…
View article: Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions
Some Functionals and Approximation Operators Associated with a Family of Discrete Probability Distributions Open
A certain discrete probability distribution was considered in [“A discrete probability distribution and some applications”, Mediterr. J. Math., 2023]. Its basic properties were investigated and some applications were presented. We now embe…
View article: An asymptotic formula for Aldaz-Kounchev-Render operators on the hypercube
An asymptotic formula for Aldaz-Kounchev-Render operators on the hypercube Open
We prove a version of a conjecture concerning the asymptotic behavior of the Aldaz-Kounchev-Render operators on the hypercube.
View article: Remarks on q-Monotone Functions and the Bernstein polynomials
Remarks on q-Monotone Functions and the Bernstein polynomials Open
We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function $$f\in C[0,1]$$ , which is twice differentiable in [0, 1], imply that the function is q -monotone. This provides …
View article: Positive linear operators and exponential functions
Positive linear operators and exponential functions Open
Using the family of generalized Baskakov operators we propose a general method to construct positive linear operators preserving exponential functions. A conjecture concerning Voronovskaja type formula and some applications are presented.
View article: Relations Between the Bernstein Polynomials and q-monotone Functions
Relations Between the Bernstein Polynomials and q-monotone Functions Open
We show that certain inequalities involving differences of the Bernstein basis polynomials and values of a function $$f\in C[0,1]$$ , imply that the function is q -monotone. In view of previous results of the authors (see the lis…
View article: Convergence of Special Sequences of Semi-Exponential Operators
Convergence of Special Sequences of Semi-Exponential Operators Open
Several papers, mainly written by J. de la Call and co-authors, contain modifications of classical sequences of positive linear operators to obtain new sequences converging to limits which are not necessarily the identity operator. Such re…
View article: Poisson approximation to the binomial distribution: extensions to the convergence of positive operators
Poisson approximation to the binomial distribution: extensions to the convergence of positive operators Open
The idea behind Poisson approximation to the binomial distribution was used in [J. de la Cal, F. Luquin, J. Approx. Theory, 68(3), 1992, 322-329] and subsequent papers in order to establish the convergence of suitable sequences of positive…
View article: A Voronovskaja type formula for Soardi’s operators
A Voronovskaja type formula for Soardi’s operators Open
In 1991 Soardi introduced a sequence of positive linear operators $$\beta _{n}$$ associating to each function $$f\in C\left[ 0,1\right] $$ a polynomial function which is closely related to the Bernstein polynomials on $$\left[ -1,+1\righ…
View article: Aldaz-Kounchev-Render operators and their approximation properties
Aldaz-Kounchev-Render operators and their approximation properties Open
The approximation properties of the Aldaz-Kounchev-Render (AKR) operators are discussed and classes of functions for which these operators approximate better than the classical Bernstein operators are described. The new results are then ex…
View article: Algebraic Systems with Positive Coefficients and Positive Solutions
Algebraic Systems with Positive Coefficients and Positive Solutions Open
The paper is devoted to the existence, uniqueness and nonuniqueness of positive solutions to nonlinear algebraic systems of equations with positive coefficients. Such systems appear in large numbers of applications, such as steady-state eq…
View article: Generalized Kantorovich modifications of positive linear operators
Generalized Kantorovich modifications of positive linear operators Open
Starting with a positive linear operator we apply the Kantorovich modification and a related modification. The resulting operators are investigated. We are interested in the eigenstructure, Voronovskaya formula, the induced generalized con…
View article: A Bernstein-Schnabl type operator: Applications to difference equations
A Bernstein-Schnabl type operator: Applications to difference equations Open
We consider a sequence of positive linear operators Ln of Bernstein-Schnabl type. It was studied in the literature from various points of view; we provide new properties of it. The eigenstructure of these operators is described. We investi…
View article: Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation
Generalized Bernstein Kantorovich operators: Voronovskaya type results, convergence in variation Open
This paper includes Voronovskaya type results and convergence in variation for the exponential Bernstein Kantorovich operators. The Voronovskaya type result is accompanied by a relation between the mentioned operators and suitable auxiliar…
View article: Modified Operators Interpolating at Endpoints
Modified Operators Interpolating at Endpoints Open
Some classical operators (e.g., Bernstein) preserve the affine functions and consequently interpolate at the endpoints. Other classical operators (e.g., Bernstein–Durrmeyer) have been modified in order to preserve the affine functions. We …
View article: Voronovskaja-Type Quantitative Results for Differences of Positive Linear Operators
Voronovskaja-Type Quantitative Results for Differences of Positive Linear Operators Open
We consider positive linear operators having the same fundamental functions and different functionals in front of them. For differences involving such operators, we obtain Voronovskaja-type quantitative results. Applications illustrating t…