Name 
Institution 
Title 
Abstract 
Radu Voichita Adriana

"BabesBolyai" University, ClujNapoca, 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 nonpositive 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 BernsteinBezier bases. This new BernsteinBezier 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 BernsteinBezier bases wi
th shape parameter $\lambda$. Some approximation properties are given, including local approximation, error estimation in terms of moduli of continuity and Voronovskajatype 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. 
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 CarmenVioleta

"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

Islamic Azad University,Talesh Branch,Talesh, Iran 
The Classification of Permutation Groups with Maximum Orbits 
Let G be a permutation group on a set O with no fixed points in O
and let m be a positive integer. If no element of G moves any subset
of O by more than m points (that is, if G
g \ G = m for every G ? O
and g ? G), and the lengths one of orbits is p, and the rest of orbits
have lengths equal to 3. Then the number t of Gorbits in O is at most
3
2
(m  1) + 1
p
. Moreover, we classifiy all groups for t =
3
2
(m  1) + 1
p
is hold.

Alshanti Waseem 
Jubail University College, Saudi Arabia 
Inequality of Ostrowski Type for Mappings with Bounded Fourth Order Partial Derivatives 
A general Ostrowski’s type inequality for double integrals is given. We utilize function whose partial derivative of order four exists and is bounded. 
Rao Nadeem 
Jamia Millia Islamia, India 
SzaszDurrmeyer operators based on Dunkl analogue 
In this article, we construct Szasz Durrmeyer type operators based on Dunkl analogue. We investigate several approximation results by these positive linear sequences, e.g. rate of convergence by means of classical modulus of continuity, uniform approximation using Korovkin type theorem on compact interval. Further, we discuss local approximations in terms of second order modulus of continuity, Peetre’s Kfunctional, Lipschitz type class and rth order Lipschitztype maximal function. Weighted approximation and statistical approximation results are discussed in the last of this article. 
Pop Emilia 
BabesBolyai University, Romania 
Calculus of the derivatives from the mean value theorem 
For two continuous functions, we study under which circumstances, the intermediate point function is differentiable of order one, two, three and four. Then, we compute the corresponding derivatives and give useful results. 
Ahasan Mohd 
Aligarh Muslim University, India 
Generalized SzászMirakjan type operators via qcalculus and approximation properties 
The aim of this paper is to construct qanalogue of generalized SzászMirakjan type
operators whose construction depend on a real valued function ρ. We prove that the
new operators provide better weighted uniform approximation over [0,∞). In terms of
weighted moduli of smoothness, we obtain degrees of approximation associated with
the function ρ. Also a Voronovskaya type result is obtained. Finally, we give some
graphical examples for these operators and show that the new operators are more flexible in view of rate of convergence to the function f which depends on the selection of ρ, u_{n,q} and v_{n,q}.

Babos Alina

"Nicolae Balcescu" Land Forces Academy, Romania 
Kepler like equation, number of solutions. 
We give a closed form solution for the number of solutions of the equation xa*sin(x)=b with a>1 and b>0. An asymptotic study of the (double) sequence of the number of solutions, when a and b are (integer) multiples of pi, is realized. As a sanitary check, a MAPLE procedure is used together with Wolfram Alpha soft.

Girjoaba Adrian

"Lucian Blaga" University of Sibiu, Romania 
Some classes of surfaces generated by blending interpolation 
We construct some classes of surfaces which satisfy some given conditions, using some interpolation operators defined on a triangle with one curved side.

Marian Daniela

Technical University of ClujNapoca, Romania 
HyersUlam stability of a general linear partial differential equation 
In this paper we will study HyersUlam stability for a general linear partial differential equation of first order in Banach space.

Ram Pratap

Delhi Technological University, Delhi 110042, India 
The family of Sz\'aszDurrmeyer type operators Involving Charlier Polynomials 
In this article, we consider Sz\'aszDurrmeyer type operators based on Charlier polynomials associated with an integral part of SrivastavaGupta operators. For such operators, we discuss some local and global approximation results by using the first and secondorder modulus of continuity, Lipchitztype space, DitzianTotik modulus of smoothness, Voronovskaya asymptotic formula, and weighted modulus of continuity.

Kozdęba Michał

University of Agriculture in Kraków, Poland 
Uniqueness of minimal projections in smooth threedimensional matrix spaces 
Let S=(M(n,m,r), .) be a threedimensional matrix space with real or complex values with a smooth norm .. We show that there is exactly one minimal projection from S into a certain subspace T and then generalize this result to the corresponding spaces of the ndimensional matrices.

Ioan Rasa

Technical University of ClujNapoca, Romania 
Composition of Positive Linear Operators 
This is a continuation of the series of six papers "On the composition and decomposition of positive linear operators IVI", initiated by Heiner Gonska. One motivation for that work was an attempt to decompose the classical Bernstein operator B_n into simpler blocks. In their unpublished manuscript "Wir schlagen Bernstein kaputt!" (2006), A. Lupas and H. Gonska introduced the operator $G_n:= \overline{\mathbb{B}}_n\circ S_{\Delta_n}$, which is in fact different from B_n, but not far from it. We survey some facts in this direction and add some new results by studying the eigenstructures of B_n, G_n, and $A_n:= S_{\Delta_n}\circ\overline{\mathbb{B}}_n$.

Paltanea Radu

Transilvania University of Brasov, Romania 
On the strong converse inequality for Bernstein operators and convex functions 
We obtain an estimate of the lower constant for Bernstein operators when they are applied to a convex function.

Moldovan Camelia Liliana, Paltanea Radu 
Transilvania University of Brasov, Romania, Transilvania University of Brasov, Romania, 
The exact form of the second moment of third degree Schoenberg spline operators 
The paper presents an explicit form for the second moment of third degree Schoenberg operators, with arbitrary knots. In particular, the case of equidistant knots is considered and estimates of approximation using moduli of continuity are obtained.

Baias Alina Ramona

Technical University of ClujNapoca, Romania 
Approximate solutions of some linear difference equations and Ulam stability 
We give some results on approximate solutions and Ulam stability for linear difference equations in Banach spaces. Moreover, we obtain sharp estimates of the Ulam constant and the best Ulam constant in some particular cases.

Otrocol
Diana

Technical University of ClujNapoca, Romania, Tiberiu Popoviciu Institute of Numerical Analisys, Romanian Academy 
Ulam stability of a linear difference equation in locally convex spaces 
We obtain a characterization of Ulam stability for a linear difference equation with constant coefficients in locally convex spaces. Moreover for the first order linear difference equation we determine the best Ulam constant.

Birou MariusMihai

Technical University of ClujNapoca, Romania. 
New positive linear operators which preserve some functions 
In this article we construct and study some positive linear operators which fix the constant functions and another function having certain properties.

Radu Miculescu

Transilvania University of Brasov, Romania. 
Iterated multifunction systems and Nadler's fixed point theorem 
We present a Nadler type result for iterated multifunction systems which represents a generalization of famous Nadler's fixed point theorem.

Popa Dorian

Technical University of Cluj Napoca, Romania. 
On Ulam stability of the linear differential operator 
We give some results on Ulam stability for the linear differential operator with constant coefficients acting in Banach spaces. Moreover, we obtain the best Ulam constant for the linear differential operator of the second order. In this way we improve and complement some recent results on this topic.

Bica AlexandruMihai

University of Oradea, Romania. 
Improved error estimate for complete quartic splines and applications 
Concerning the Hermite type complete quartic spline with deficiency 2, we improve the interpolation error estimate stated in J. Approx. Theory 58 (1989) 5867 in terms of the modulus of continuity and in the case of Lipschitzian functions. The estimate is extended by the first half part of the grid subintervals to the whole interval. Some applications of the associated corrected Simpson quadrature rule are presented including an efficient numerical method for the clamped beam fourth order differential equation.

Aristidis Tsiolikas, Ana Acu, Foteini Vakoutsi, and John Kechagias 
University of Thessaly, Greece 
Plasma arc cutting process optmization using soft computing and NN modeling 
In this work experimental data were used to train a feed forward back propagation neural network (FFBPNN) in order to predict the qu ality indicators of the plasma arc cuttng (PAC) process. Nine (9) different neural net works were developed and tested according to Taguchi orthogonal array. Analysis of means (ANOM) and the analysis of variances (ANOVA) were utilized to optimize the parameter settngs o f the NN model for better prediction performance. 
Gheorghiu CalinIoan 
Tiberiu Popoviciu Institute of Numerical Analysis, ClujNapoca, Romania. 
On the utility of nonclassical orthogonal polynomials. Boundary value and eigenvalue problems. 
In this talk we are concerned with nonclassical orthogonal polynomials as basis functions in solving, mainly, boundary value and eigenvalue problems on unbounded intervals. We analyse spectral collocation methods based on these polynomials. Some benchmark problems are considered. The usefullness of these polynomials is compared with that of classical ones, i.e., Hermite, Lagrange and mapped Chebyshev as well as with that of sinc functions. 
Gancho Tachev 
University of Architecture Civil Engineering and Geodesy, Bulgaria. 
On some modified Post Widder Operators 
In the present paper, we consider PostWidder operators and its modified form which preserve the test function x^r. We estimate direct results in terms of modulus of continuity for the modified operators. Also, some estimates for polynomially bounded functions and linear combinations are considered. The talk is based on join research with prof. Vijay Gupta

Vlad CiobotariuBoer 
"Aram Iancu" High School, ClujNapoca, Romania. 
New Integral Inequalities of Perturbed Trapezoidal Type for MTConvex Functions via Classical Integrals and Fractional Integrals 
In this paper we establish some new general integral inequalities for twice differentiable functions of which second derivatives in modulus are MTconvex via classical integrals and RiemannLiouville integrals, respectively.

Simian Dana 
"Lucian Blaga" University of Sibiu, Romania. 
On an Approach to Perform Semantic Search in a FullText Articles Data Base 
This article proposes a solution for natural language semantic searching in a fulltext articles or books database, in a process similar to fingerprinting. The proposed solution exploits the sparse distributed representation of the information in human’s brain. Using a large text corpus of articles or books, we train a neural network in order to produce a vector space of several hundred dimensions, with each unique word in the corpus being assigned a corresponding vector in the space. The word vectors are then mapped to sparse matrices. A sparse matrix corresponding to a search phrase is obtained by adding the sparse matrices associated to each word in the phrase. Based on the proposed solution, we present a proof of concept software system that allows natural language semantic searching in a fulltext article/book database. The proposed approach for semantic search does not need labeled data and could be used across languages.

Agratini Octavian, Harun Karsli 
"BabesBolyai" University, Cluj Napoca, Romania, Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy,
Bolu Abant Izzet Baysal University, Turkey. 
NonNewtonian Calculus and Approximation Theory 
Our aim is to bring multiplicative calculus to the attention of researchers working in the field of positive approximation processes. Starting from a linear positive Markov process of discrete type, we modify it using this type of calculus. Within this approach, a convergence property and an upper bound of the error of approximation are established. At the end, a particular case concerning the classical Bernstein operators is presented.

Manav Nesibe 
Gazi Üniversitesi, Turkey. 
On approximation of bivariate genuinetype operators based on Lupaş functions 
The purpose of this study is to extend the study of Lupaş based operators introduced by Lupaş (1995). In our study we consider a bivariate generalization of the operators defined by Agratini (1999). We give some approximation properties, including local approximation, error estimation in terms of modulus of continuity, and some results. Finally, we give some visual examples about the convergence of our operators to f(x).

Anastassiou George 
University of Memphis, Tennessee, USA. 
On my life and work 
CELEBRATING GEORGE ANASTASSIOU 500 RESEARCH PUBLICATIONS REVIEWED AND INDEXED AT AMS/MATHSCINET AND ZENTRALBLATT AND COUNTING, A USUALLY UNSURPASSED RECORD INTERNATIONALLY!

Guran Liliana 
"Vasile Goldis" Western University of Arad, Romania 
On some new multivalued results in the metric spaces of
Perov's type 
The purpose of this paper is to present some new fixed point results in the generalized metric spaces of Perov's sense under a contractive condition of HardyRogers type. The data dependence of the fixed point set, the wellposedness of the xed point problem, as well as, the UlamHyers stability are also studied.

Miclaus Dan 
Technical University of ClujNapoca, North University Center at Baia Mare, Romania 
The classical Bernstein polynomial involved in a root finding method 
One of the most important problem in all the history of mathematics was to solve the nonlinear equation f(x)=0. We can not find always an accurate solution of this equation, but applying a root finding method we can get some good approximations. In this talk we focus on a root finding method which has as start point the classical Bernstein polynomial.

Madalina Dancs, Maduta AlexandraIoana, 
Technical University of ClujNapoca, Romania 
Entropies for some continuous distributions of probabilities 
We consider classical entropies associated with several
continuous distributions of probabilities. Explicit expressions and properties of them are presented.

Karsli Harun

Bolu Abant Izzet Baysal University, Faculty of Science and Arts, GolkoyBolu, Turkey 
Some new results on Urysohn type operators 
In the present work, which is a continuation of recent studies of the author, we focus our attention on the generalization and extension of representing or reconstruction of functions (or signals) to operators by means of Urysohn type operators. Since the Urysohntype operators contains some wellknown integral operators, which frequently used to solve many problems in engineering, physics and approximation problems, this type of operators are very useful and important for di?erent sciences and hence it need deep investigation. In particular, we give some characterization of newly introduced Urysohn type operators constructed by using the Urysohn type operator values instead of the rational sampling values of the function (or signal). This way, in some cases the new operators are more ?exible than the classical ones and we will investigate some convergence problems for them.

Tincu Ioan, Sofonea Florin 
"Lucian Blaga" University of Sibiu, Romania 
On an inequalit y for Legendre p olynomials 
We know that the Legendre polynomials P_n(x), satisfy the inequality 1P_n(x)>0 $ for every x from [1,1]. In this paper we determine two polynomials, expressed using the Chebyshev polynomials of the first and second kind, which verify: Alpha_n(x)<1P_n(x)<Beta_n(x)$ for every n
and x in [1,1]. 
Popa C. Emil 
"Lucian Blaga" University of Sibiu, Romania 
A note on Jordan’s inequality 
We present some upper and lower bounds for the functions sin(x)/x. This bounds are polynomials of degree 2n1 where n is any nonnegative integer.

Popescu (Curila) Diana 
University of Oradea 


Satmari Zoltan 
University of Oradea 


