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One studies simultaneous approximation properties of fundamental Bernstein polynomials involved in the construction of the mentioned operators. [ABSTRACT FROM AUTHOR]

The paper is the English variant, with additional remarks, of two earlier papers published by the author in Romanian, many years ago. It is motivated by the fact that in the last years many mathematicians were interested on the subject and they can't found copies of acceptable graphic quality. In the paper we introduce the notions of convex sequence of p order (p being a positive integer) and respectively system of subconvex sequence of first order. One proves that any subconvex sequence of second order and any system of subconvex sequences of first order are convergent. [ABSTRACT FROM AUTHOR]

The paper has a methodical content and is addressed to young researchers. Its main goal is to prove how the property of monotonicity can be transferred from the sequence of univariate Bernstein polynomials to those of bivariate Bernstein polynomials. Let ퟙ be the set of positive integers, m; n ∈ ퟙ, I = [0; 1], I2 = [0, 1] × [0, 1], ℝI2 = {f∣f : I2 → ℝ}, C(I2) = {f ∈ ℝI2 ∣f continuous on I2}. Denote by Bm,n : C(I2) → C(I2) the Bernstein bivariate operator. This operator associates to each function f ∈ C(I2) the bivariate Bernstein polynomial Bm,n(f; x,y). It is well known that the sequence {Bm,n(f; x, y)}m,nℝퟙ converges to f, uniformly on I2 for each f ℝ C(I2). In the present paper one investigates the monotonicity of the sequence {Bm,n(f; x, y)}m,nℝퟙ. One proves that if f ℝ C(I2) is convex of (1; 1)-order on I2 the sequence {Bm,n(f; x, y)}m;nℝퟙ is monotonous decreasing and Bm,n(f; x, y) ≥ f(x, y), (∀) (x, y) ℝ I2. [ABSTRACT FROM AUTHOR]

Let a,b,c,d ∊R be given such that a

In the present paper we introduce the GBS (Generalized Boolean Sum) operators of Durrmeyer type based on q -integers and the approximation of B-continuous functions using the above operators is studied. In addition, a uniform convergence theorem is established and the degree of approximation in terms of mixed modulus of continuity is evaluated. The study contains in the last section numerical considerations regarding the constructed operators based on MATLAB algorithms. [ABSTRACT FROM AUTHOR]

The aim of this paper is to pay a modest homage to the world class researcher Professor Dimitrie D. Stancu, well known for the classes of linear positive operators he introduced and studied, which have influenced, are still influencing and will influence the future development of approximation theory. [ABSTRACT FROM AUTHOR]

The goal of this paper is to introduce new q-Stancu-Kantorovich operators and to study some of their approximation properties. A convergence theorem using the well known Bohman- Korovkin criterion is proven and the rate of convergence involving the modulus of continuity is established. Furthermore, a Voronovskaja type theorem is also proven. [ABSTRACT FROM AUTHOR]

To study approximation properties of linear positive operators various identities involving divided differences are used. The aim of this note is to present two types of such kind of identities. The first one was used by Abel and Ivan [Abel, U. and Ivan, M., Some identities for the operator of Bleimamm, Butzer and Hahn involving divided differences, Calcolo, 36 (1999), 143-160; Abel, U. and Ivan, M., New representation of the remainder in the Bernstein approximation, J. Math. Anal. Appl., 381 (2011), No. 2, 952-956] to derive approximation properties of Bleimann, Butzer and Hahn (BBH) operators from the corresponding properties of the classical Bernstein operators. The second type of identifies can be used to derive some approximation properties of the BBH operators from the properties of some Stancu type operators. [ABSTRACT FROM AUTHOR]