Dan Miclaus

North University of Baia Mare - Romanian

On the monotonicity property for the sequence of Stancu type polynomials

This note presents the proof of the monotonicity property for the sequence of Stancu type polynomials, involving divided differences and convex functions. As an application we get the form of remainder term associated to the Stancu type operators applying the Popoviciu's Theorem.

Some Results for Genuine Szasz-Mirakjan-Durrmeyer Operators

We present commutativity properties of the operators as well as the commutativity with an appropriate differential operator and a strong converse result of type A in terms of a K-functional with an explicit constant. Together with a direct theorem this leads to an equivalence result for the error of approximation and the K-functional

On linear combinations of the Phillips operator

We establish a Voronovskaja's type estimate for the linear combinations of the Phillips operator. This improves the previous results on this topic of C.May, R.Agrawal, V.Gupta etc. This is a joint work with M.Heilmann from the University of Wuppertal, Germany.

On a mean value theorem of T.M. Flett

Sequential Optimality Conditions for Variational Inequalities

In the characterizations of the solutions of the variational inequalities (via gap functions or by means of the subdifferential), the fulfillment of a regularity condition was of great importance. We show in this presentation that even in the absence of a regularity condition, we can still characterize these solutions. We use as tool the sequential optimality conditions given by Bot, Csetnek and Wanka. Several examples are illustrating the theoretical aspects. This is a joint work with Ernö Robert Csetnek from Technical University, Chemnitz, Germany.

Characterizations for epsilon-duality gap statements for constrained convex optimization problems

In this material we present different regularity conditions that equivalently characterize various epsilon-duality gap statements for constrained convex optimization problems and their Lagrange and Fenchel-Lagrange duals in separated locally convex spaces. These regularity conditions are formulated by using epigraphs and epsilon-subdifferentials. This material is a work joint with dr. Sorin-Mihai Grad, from Technical University, Chemnitz, Germany.

New Wolfe and Mond-Weir type vector duality

We introduce new vector duals attached to a general vector optimization problem and we formulate duality results. These vector duals were obtained by exploiting an idea due to W. Breckner and I. Kolumbian and with the help of Wolfe and Mond-Weir scalar duals for general optimization problems proposed by R.I. Bot and S.-M. Grad. Acknowledgement. UBB, Research supported by project POSDRU88/1.5/S/60185. This is a joint work with Dr. Sorin-Mihai Grad from Technical University, Chemnitz, Germany.

On infinite products of positive linear operators

Infinite products of positive linear operators reproducing linear functions are considered from a quantitative point of view. Refining and generalizing convergence theorems of Gwozdz-Lukawska, Jachymski, Gavrea, Ivan and the present authors, it is shown that infinite products of certain positive linear operators, all taken from a finite set of mappings reproducing linear functions, weakly converge to the first Bernstein operator. A discussion of products of Meyer-Konig and Zeller operators is included. The talk is based upon joint work with Ioan Rasa (UT Cluj).

Approximation properties of some bidimensional Bernstein-Durrmeyer operators

We consider a class of sequences of positive linear operators on a symplex of Durrmeyer type, depending on a general weight. These operators have good properties of approximation

Generalized Characterization Theorem for the K-functional Associated with the Algebraic Version of Trigonometric Jackson Integrals

The purpose of this paper is to present a characterization of a certain Peetre K-functional in
Lp[-1,1] norm by means of a modulus of smoothness. We generalize the earlier chracterization of Ivanov and extend the result to a more general setting.

First order approximated semi-infinite optimization problems

In this paper, we consider the semi-infinite optimization problem which I attach the first order approximate problem. Relationships are established between the feasible sets of the two issues and then between their optimal solutions.

Differential complementarity problems and collision free trajectories

We present how differential complementarity problems(DCPs) can be used in generating collision free trajectories. We address issues related to robust and optimal control. The applications are in the area of autonomous navigation.

Some remarks on the generalized Euler sequence

We provide a highly convergent version of the generalized Euler sequence and find the element with the optimal rate of convergence in several classes of sequences with imposed form.

Some remarks on the generalized Euler sequence

We provide a highly convergent version of the generalized Euler sequence and find the element with the optimal rate of convergence in several classes of sequences with imposed form

Remarks on Bernstein-Euler-Jacobi type operators

We introduce and study a class of positive linear operators defined as a composition (two Bernstein and a Euler-Jacobi Beta operator in the middle) that reduces in special cases to many known operators. Using the method presented by Z. Finta we prove direct and converse inequalities of type A in terms of a K-functional. This is done for two special cases, that is, for the composition of two different Bernstein operators and for a particular case of the general composition that reproduces linear functions.

Gruess-type inequalities for the BLaC operator

The classical form of Gruess' inequality gives an estimate of the difference between the integral of the product and the product of the integrals of two functions in C[a,b]. On the other hand, BLaC-wavelets ("Blending of Linear and Constant wavelets") were introduced by G.P. Bonneau, S. Hahmann and G. Nielson in 1996 and describe a compromise between the sharpness of the Haar wavelets and the smoothness of the linear ones.
The aim of this presentation is to discuss Gruess-type inequalities for the BLaC operator. Using a result of Gonska et al., a quantitative Chebyshev-Gruess-type inequality is obtained in terms of the least concave majorant of the classical modulus of continuity. Interesting is how the blending parameter influences our results.

A method for solving a kind of bilevel discrete programming problem

In the present paper a numerical method for solving a particular type of bilevel discrete programming problem is given. This particular kind of problem is get as a result of mathematical modeling of an budget allocation problem corresponding to professional training of the unemployed persons. This paper is a joint work with Luciana Neamtiu from Oncology Institute Prof. Dr. I. Chiricuta (Cluj Napoca)

Some approximations properties of a Schurer-Bernstein operators based on q integers

We consider the class of generalized Schurer Berntstein operators in q calculus for which some properties of monotonicity and convexity are studied. The paper contain also numerical representation of these operators, based on Matlab algorithms and iterative relations of basic functions.

A note on discrete operators and their associated integral operators

We provide an estimation of the difference between discrete operators and their associated integral operators. A lot of examples are given

On the Approximation of Analytic Functions by Complex Bernstein-Type Operators in Compact Discs

We aim to prove a general result related to the uniform convergence of certain Bernstein-type operators attached to an analytic function in a compact disc

Some corrected optimal quadrature formulas in sense Nikolski and error bounds

In recent years some authors have considered so called perturbed (corrected) quadrature rules. By corrected quadrature rule we mean the formula which involves the values of the first derivative in end points of the interval not only the values of the function in certain points. We consider the corrected quadrature rules of some optimal quadrature formulas in sense Nikolski and the estimations of error involving the second derivative are given. The numerical examples which provides that the approximation in corrected rule of a optimal quadrature formula in sense Nikolski is better than in the original rule are considered.

Characterization theorems of Jacobi polynomials

The aim of this paper is to prove Turans inequality and equality concerning the roots of the Jacobi polynomial.

An extension of the Riemann-Lebesgue Lemma for Chebyshev polynomials

The classical Riemann-Lebesgue Lemma corresponding to Fourier basis is extended to Chebyshev polynomials of the first kind.

About Four Convergences to e and 1/e

We give the shortest proof of the classical two sided estimation of the standard convergence to e.We also give the similar results for three other convergences, we show the equivalence of all these and we give a mnemonic rule.

Localization properties of some composite multivariate operators

We study the localization properties of several sequences of multivariate linear positive operators. In particular we analyze the case of operators obtained by composition which present special localization behavior

Applications of the impruved Fejer’s sum

In this paper, using the quadrature formulas of Bouzitat type, we present an improvement of Fejer's inequality and also some applications

Bounds to a sequence which use Euler's constant

The aim of this paper is to improve an inequality which characterizes the order of convergence of the sequence En = 1 + 1/1! + 1/2! + ... + 1/n! to the limit e.

Evaluations of the remainder using devided differences

Our aim is to find evaluation of the remainder using devided differences, starting point of research given below it the result of O. Arama.

Complete monotonicity and estimates for gamma function

The aim of this work is to show how the theory of completely monotonic functions can be used to establish estimates for gamma and related functions