Related papers: Lagrange-type operators associated with $U_n^{\var…
We study power series of members of a class of positive linear operators reproducing linear function and constituting a link between genuine Bernstein-Durrmeyer and classical Bernstein operators. Using the eigenstructure of the operators we…
The present paper deals with the estimate of the differences of certain positive linear operators and their derivatives. Our approach involves operators defined on bounded intervals, as Bernstein operators, Kantorovich operators, genuine…
In this paper, we introduce a new class of positive linear operators that generalize the classical Bernstein operators. Specifically, we construct a sequence of operators that reproduce the logarithmic function $\ln(1+\mu+x)$, with $\mu >…
We define the associated geometric series for a large class of positive linear operators and study the convergence of the series in the case of sequences of admissible operators. We obtain an inverse Voronovskaya theorem and we apply our…
Many well-known positive linear operators (like Bernstein, Baskakov, Sz\'{a}sz-Mirakjan) are constructed by using specific fundamental functions. The sums of the squared fundamental functions have been objects of study in some recent…
In the present article, we propose the new class positive linear operators, which discrete type depending on a real parameters. These operators are similar to Jain operators but its approximation properties are different then Jain…
The central problem in this technical report is the question if the classical Bernstein operator can be decomposed into nontrivial building blocks where one of the factors is the genuine Beta operator introduced by M\"uhlbach and Lupa\c{s}.…
We construct and study sequences of linear operators of Bernstein-type acting on bivariate functions defined on the unit disk. To this end, we study Bernstein-type operators under a domain transformation, we analyse the bivariate…
We introduce a new type of Bernstein operators, which can be used to approximate the functions with inner singularities. The direct and inverse results of the weighted approximation of this new type of combinations are given.
This paper investigates the composition of Bernstein--Durrmeyer operators and Sz\'asz--Mirakjan--Durrmeyer operators, focusing on the structure and properties of the associated kernel functions. In the case of the Bernstein--Durrmeyer…
Positive polynomial operator that approximates Urison operator, when integration domain is a "regular triangle" is investigated. We obtain Bernstein Polynomials as a particular case.
The eigenvalues of a self-adjoint nxn matrix A can be put into a decreasing sequence $\lambda=(\lambda_1,...,\lambda_n)$, with repetitions according to multiplicity, and the diagonal of A is a point of $R^n$ that bears some relation to…
We introduce the class of functions positively associated with a linear operator. We describe these classes for several integral operators including the $q$-cosine transform and the spherical Radon transform. We show that positively…
The aim of this paper is to study variation detracting property and con- vergence in variation of the Bernstein-Durrmeyer modifications of the classical Bernstein operators in the space of functions of bounded variation. These problems are…
In the present paper, the authors introduce and investigate new sequences of positive linear operators which include some well known operators as special cases. Here we estimate the rate of convergence for functions having derivatives of…
This note discusses how an operator analog of the Lagrange polynomial naturally arises in the quantum-mechanical problem of constructing an explicit form of the spin projection operator.
In this paper, we investigate the power of nearly purely operational techniques in the study of umbral calculus. We present a concise reconstruction of the theory based on a systematic use of linear operators, with particular attention to…
In this work we introduce interesting infinite series, related to Ramanujan-Soldner constant. Our method uses general properties of polynomials of binomial type and Lagrange inversion theorem. Also we study properties of the operator…
The present paper deals with modifications of Bernstein, Kantorovich, Durrmeyer and genuine Bernstein-Durrmeyer operators. Some previous results are improved in this study. Direct estimates for these operators by means of the first and…
We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…