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Plenary Speakers

Ioan Rasa (Tehnical University Cluj-Napoca, Romania)
Gancho Tachev (University of Architecture Civil Engineering and Geodesy, Bulgaria)

Participants
Name Institution Title Abstract
"Babes-Bolyai" University, Cluj-Napoca, Romania
Approximation by Bernstein Type Operators
In 1912 Bernstein introduce his famous operators in order to prove the Weierstrass approximation theorem. Starting with the approximation properties of Bernstein operators, in the present paper we construct two representations for Inverse Bernstein operators and discuss about asymptotic convergence. We apply a general Voronovskaja type formula, suitable for non-positive operators. In the second part, we extend the study of Bernstein operators by one of his generalization namely $\lambda$-Bernstein operators. This operators was introduce by Cai, Lian and Zhou in 2018 and use a new Bernstein-Bezier bases. This new Bernstein-Bezier bases were introduced by Ye, Long and Zeng in 2010, in order to obtained more flexibility by adding the shape parameter $\lambda$. When $\lambda=0$, they reduce to Bernstein fundamental polynomials. In our paper we consider a generalization of the $U^{\rho}_n$ operators introduced in 2007 by Paltanea, using the new Bernstein-Bezier bases wi th shape parameter $\lambda$. Some approximation properties are given, including local approximation, error estimation in terms of moduli of continuity and Voronovskaja-type asymptotic formulas. Finally, we give some numerical examples and graphs to put in evidence the convergence of our studied operators..
Ratiu Augusta
"Lucian Blaga" University, Sibiu, Romania, "Lucian Blaga" University of Sibiu, Romania
Constraint method for vector optimization problems
In this paper, we consider a vector optimization problem. To obtain information about the efficient solutions of this problem we use constraint method. Some graphical representations are given to illustrate the efficient values.
Muraru Carmen-Violeta
"Vasile Alecsandri" University of Bacau, Romania
Some approximation properties by a class of bivariate operators
Starting with the well known Bernstein operators, in the present paper we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely the Generalized Boolean Sum (GBS) in the Bogel space of continuous functions is given. In order to underline the fact that in this particular case GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also the error of approximation for the modified Bernstein operators and its GBS type operator are compare.
Minculete Nicusor
Transilvania University of Brasov, Romania
Inequalities in an 2 - inner product space
Starting with the well known Bernstein operators, in the present paper we give a new generalization of the bivariate type. The approximation properties of this new class of bivariate operators are studied. Also, the extension of the proposed operators, namely the Generalized Boolean Sum (GBS) in the Bogel space of continuous functions is given. In order to underline the fact that in this particular case GBS operator has better order of convergence than the original ones, some numerical examples are provided with the aid of Maple soft. Also the error of approximation for the modified Bernstein operators and its GBS type operator are compare.
Behname Razzaghmaneshi