Name 
Institution 
Title 
Abstract 
ACU Ana Maria 
"Lucian Blaga" University of Sibiu, Romania 
Approximation properties of the modified Stancu operators

Abstract: In this paper we construct a sequence of Stancu type operators which
are based on a function $\tau$. This function is any function on
$[0,1]$ continuously differentiable $\infty$ times, such that
$\tau(0)=0$, $\tau(1)=1$ and $\tau^{\prime}(x)>0$ for $x\in [0,1]$.
Note that the Korovkin set $\{1, e_1, e_2\}$ is generalized to
$\{1,\tau,\tau^2\}$ and these operators present a better degree of
approximation then the original ones. We give a direct approximation
theorem by means of the DitzianTotik modulus of smoothness and a
Voronovskaja type theorem by using the DitzianTotik modulus of
smoothness. 
Radu Voichita Adriana,
Acu Ana Maria

"BabesBolyai" University, ClujNapoca, Romania, "Lucian Blaga" University of Sibiu, Romania

About the iterates of some operators depending on a parameter 
During the last decade, qCalculus was intensively used for the construction of various generalizations of many classical linear and positive operators. The aim of this paper is to study the convergence of the iterates of some positive linear operators depending on a parameter, using contraction principle (the weakly Picard operators theory) and _rst and second moduli of continuity(some quantitative results). Also some applications of di_erent kind of linear and positive operators are provided.

Muraru Carmen Violeta 
"Vasile Alecsandri" University of Bacau, Romania 
Some Approximation Properties of a Durrmeyer variant of qBernsteinSchurer Operators 
Our goal is to present approximation theorems for a Durrmeyer variant of qBernsteinSchurer
operators defined by C.V. Muraru and modified by M.Y. Ren and X.M. Zeng. C.V. Muraru
and A.M. Acu studied the Durrmeyer variant of the original qBernsteinSchurer using uniform
convergence. Our choice is to use both the uniform convergence and the statistical convergence
to establish some approximation theorems for a Durrmeyer variant of the modified qBernstein
Schurer operators. 
Naokant Deo 
Delhi Technological University (Formerly Delhi College of Engineering), India 
Modified Durrmeyer Operators Based On Inverse PolyaEggenberger Distribution 
In this contribution we consider modified Durrmeyer operators associated to inverse P\' olyaEggenberger distribution. First, we give the moments of our operators and then study approximation properties of these operators which include uniform convergence and degree of approximation. 
Octavian Agratini 
Babes  Bolyai University, Cluj  Napoca, Romania 
Recent results on linear and positive operators 
Our speech targets two aspects.
Firstly we deal with a general class of linear approximation processes designed using series. The main goal is to identify functions for which these operators provide uniform approximation over unbounded intervals.
Secondly, starting from positive linear operators which have the capability to reproduce affine functions, we construct integral operators of Kantorovichtype which enjoy by the same property. We focus to show that the error of approximation can be smaller than in classical Kantorovich construction on some subintervals of its domain.
In both research directions, particular cases are highlighted. 
Gupta Vijay 
Netaji Subhas Institute of Technology, New Delhi, India 
Some problems in approximation by linear positive operators 
. 
Alina Babos 
"Nicolae Balcescu " Land Forces Academy, Sibiu, Romania 
Interpolation operators on a square with one curved side 
We construct some Lagrange, Hermite and Birkhofftype operators, which interpolate a given function and some of its derivatives on the border of a square with one curved side. We also consider their product and Boolean sum operators. We study the interpolation properties and the degree of exactness of the constructed operators. 
BascanbazTunca Gülen,
Ayşegül Erençin, Fatma Taşdelen

Ankara University, Turkey
Abant İzzet Baysal University 
Some properties of Bernstein type Cheney and Sharma operators 
In this talk, we show that Bernstein type Cheney and Sharma operators preserve modulus of continuity and Lipschitz continuity properties of the attached function f. We also give a result for these operators when f is a convex function. 
Akkus Ilker 
Kirikkale University, Turkey 
On some combinatorial identities 
We present some closed forms for sums involving the binomial coefficients, Fibonacci and Lucas numbers in terms of the falling factorial. 
Ömür Nese 
Kocaeli University, Turkey 
On the matrices with the genealized hyperharmonic numbers of order r 
In this paper, we define two n×n matrices A_{n} and B_{n} with a_{i,j}=H_{i,j}^{r} and b_{i,j}=H_{i,m}^{j}, respectively, where H_{n,m}^{r} are a generalized of hyperharmonic numbers of order r. We give some new factorizations and determinants of the matrices A_{n} and B_{n}. 
Kizilaslan Gonca 
Kirikkale University, Turkey 
Matrix representation of some binomial identities 
We present a new perspective to the matrix representation and show that the sums of the some binomial sequences could be evaluated directly using this representation. 
Koparal Sibel 
Kocaeli University, Turkey 
Some congruences with balancing and Lucasbalancing numbers 
In this paper, we present new congruences involving balancing and cobalancing numbers. 
Gavrea Bogdan 
Technical University of ClujNapoca, Romania 
Stochastic complementarity problems for a class of rigid body systems 
We consider a class of rigid body systems in a quasistatic setting. The goal is to plan and control such systems in the presence of uncertainties that are due to model formulation, parameter estimation or inexact measurements. The rigid body system is modeled using complementarity problems, which by adding the uncertainty element give rise to stochastic complementarity problems. In this talk, both theoretical and numerical issues will be addressed. 
Tuncer Acar, Ali Aral 
Kirikkale University, Turkey 
Bernstein operators which preserve exponential functions 
This speech is devoted to a modification of Bernstein operators which fix the functions 1 and e^{2\alpha x} \alpha>0). Our aim in this construction is to obtain better approach with Bernstein operators. We investigate uniform convergence of new constructions and present the rate of convergence via modulus of continuity. Using generalized convexity, we examine shape preserving properties of the operators. The comparisons of new constructions with classical Bernstein operators are also discussed, graphical examples to show the flexibility of new operators are presented as well. 
Özlem Acar, Ishak Altun 
Kirikkale University, Turkey 
On some fixed point results in metric spaces endowed with a graph 
In this talk, we give some fixed point theorems considering FGcontraction on metric spaces with a graph. Some illustrative examples are also presented to show the importance of graph on the contractive condition. 
Sule Yüksel Güngör, Nurhayat Ispir 
Gazi University, Turkey 
Shape Preserving Properties of Generalized Szász Operators of MaxProduct Kind 
In this study, we present the nonlinear generalized Szász operators of maxproduct kind and we give a better error estimate for the large subclasses of functions. Also we study some shape preserving properties of concerned operators. 
Müzeyyen Özhavzali, Ayhan Aydin 
Kirikkale University, Atilim University, Turkey 
A Comparison for Some Linear Positive Operators by calculating the errors in the Approximation 
In this paper, we give a Korovkintype approximation theorem for sequences of positive linear operators on the space of all continuous real valued functions defined on [a,b]. We also give convergence and approximation properties of a Chlodowsky type generalization of Stancu polynomials called StancuChlodowsky polynomials. We made a comparison between the approximations obtained by the generalized Bernstein operator and the StancuChlodowsky polynomials by calculating the errors in the approximations. Figures and numerical results verify the theoretical results. 
Minculete Nicusor 
Transilvania University of Brasov, Romania 
A note on two inequalities with the convex
functions 
In this note we present two inequalities with the convex functions which
improves Young's inequality. Also we obtain several applications of these inequalities. 
Luca Traian Ionut 
Babes Bolyai University, Romania 
Bicriteria problems for energy optimization 
In this material we consider a new approach for energy optimization based on bicriteria problems. Similar method was successfully developed for portfolio theory. We managed to extend and improve it. Due to optimization for energy production which has an important impact on greenhouse gases, our models bring some contributions to General Climate Models. 
Trapti Neer , Ana Maria Acu and P.N. Agrawal 
Indian Institute of Technology Roorkee,India; "Lucian Blaga" University of Sibiu, Romania 
Degree of approximation by Chlodowsky variant oj JakimovskiLeviatanDurrmeyer type operators 
In this paper we introduce the Chlodowsky variant of the Durrmeyertype Jakimovsky Leviatan operators. We give the rate of approximation in terms of first order modulus of continuity and the DitzianTotik modulus of smoothness. Also we introduce a Voronovskajatype asymptotic formula. In the last section we give some approximation results for a weighted space. 
P.N. Agrawal 
Indian Institute of Technology Roorkee,India 
BernsteinSchurerKantorovich operators based on (p,q)integers 
The purpose of the present paper is to introduce the (p, q)analogue of BernsteinSchurerKantorovich operators by means of (p, q)Jackson integral. We obtain the Korovkin type approximation theorem and estimate the rate of convergence in terms of the modulus of continuity and by means of Lipschitz class function. Subsequently, we define the bivariate case of these operators and estimate the rate of convergence in terms of the partial modulus of continuity, complete modulus of continuity and the degree of approximation by using Peetre’s K functional and the Lipschitz class. In the last section, we define the associated GBS (Generalized Boolean Sum) operators and study the degree of approximation of B¨ogel continuous and B¨ogel differentiable functions with the aid of the mixed modulus of smoothness. Furthermore, we illustrate the convergence of the (p, q)BernsteinSchurerKantorovich operators for one and two dimensional cases to certain functions by graphics using Maple algorithm and also show the comparison of the convergence of these operators visavis BernsteinSchurer and BernsteinKantorovich operators based on (p, q)integers. 
AdoniaAugustina Opris 
Technical University of ClujNapoca, Romania 
A class of Aczel  Popoviciu type inequality 
In this paper we give new generalized and sharpend version of Aczel  Popoviciu inequality via positive and homogeneous functionals. 
Dilek Soylemez Ozden 
Ankara University, Turkey 
On Uniform Approximation by Modified qBleimann, Butzer and Hahn Operators 
In this work, we consider a generalization of the sequences of qBleimann, Butzer and Hahn
operators, which are based on a function ρ. We study uniform approximation of such a sequence. We also obtain degree of approximation. Further, we investigate monotonicity properties of the sequence of operators.

Albu Toma 
Simion Stoilow Institute of Mathematics of the Romanian Academy, Bucharest 
The conditions (C_i) in rings, modules, categories, and lattices 
In this talk we present the latticial counterparts of the conditions (C_i), i = 1, 2,3,11,12, for modules. In particular, we discuss the lattices satisfying the condition (C_1) we call CC lattices (for Closed are Complements), i.e., the lattices such that any closed element is a complement, that are the latticial counterparts of CS modules (for Closed are Summands). Applications of these results are given to Grothendieck categories and module categories equipped with a torsion theory.

Arikan Talha 
Hacettepe University, Turkey 
Evaluating Some Hessenberg Determinants via Generating Functions 
In this work, we will use generating function method to determine the relationships between determinant of a class of Hessenberg matrices whose entries are consist of terms of certain number sequences, and, their generating functions. Moreover we will de…fine two new classes of Hessenberg matrices whose determinants have not been computed before. Finally, we give an elegant method to compute determinants of Hessenberg matrices whose entries are consist of terms of general linear recursive sequences.

Kara Yeliz 
Hacettepe University, Turkey 
pextending Modules with Abelian Endomorphism Rings 
A module M is called pextending if every projection invariant submodule of M is essential in a direct summand of M. We focus our attention on pextending modules to show that under some module theoretical conditions on this class of modules with Abelian endomorphism rings have indecomposable decompositions. This is a joint work with Adnan Tercan.

Karsli Harun 
Abant Izzet Baysal University, Turkey 
Approximation problem for certain linear positive operators that approximate the Urysohn type operator 
The goal of this study is generalization and extension of the theory
of interpolation of functions to functionals and operators. We investigate the
convergence problem for linear positive operators that approximate the Urysohn type
operator in some functional spaces. One of the main difference between the
present work and convergence to a function lies in the use of the Urysohn type
operator values instead of the sampling values of a function. From the definitions
of the Urysohn type operators, Heaviside and Dirac Delta function, the current
study can be also consider as convergence of a kind of nonlinear form of the
classical linear positive operators to a function.

Zapryanova Teodora 
University of EconomicsVarna, Bulgaria 
On the Iterates of Continuous Linear Operators Preserving Constants and Jackson type Operator Gs 
In this paper we study the limit of the iterates of a large class of linear bounded operators preserving constants. We obtain in addition the limit of the iterates of algebraic version of the trigonometric Jackson integrals. The proofs are based on spectral theory of linear operators.

Vlad CiobotariuBoer 
"Avram Iancu" High School, ClujNapoca, Romania 
Some New Integral Inequalities for Twice Diffenetiable Functions 
We establish some new general integral inequalities for twice differentiable functions. Then we apply these inequalities for special means of real numbers and new general quadrature rules of trapezoidal
type.

Ghisa Dorin 
"York" University, Toronto, Canada 
Partial Euler Products and the Great Riemann Hypothesis 
We are studying general Dirichlet series having the abscissa of convergence less than 1/2 and which can be continued analytically to the whole complex plane. When the conformal mappings of the corresponding fundamental domains can be approximated by partial Euler products, then the non trivial zeros of the respective functions have all the real part 1/2.

Gheorghiu CalinIoan 
Romanian Academy, "T. Popoviciu" Institute of Numerical Analysis, ClujNapoca, Romania 
Two distinct ways to introduce the Chebyshev polynomials. 
We comment on an elementary but fairly constructive way to introduce the classical Chebyshev polynomials due to Tiberiu Popoviciu (On the Best Approximation of Continuous Functions by Polynomials. Five lessons held at the Faculty of Science from Cluj during the academic year 19331934). Accordingly, the most important properties of these polynomials are obtained. Then we compare this strategy with the well known one which considers Chebyshev polynomials as solutions of a singular SturmLiouville eigenvalue problem.

Tercan Adnan 
Hacettepe University, Turkey 
pextending Modules with Abelian Endomorphism Rings 

Mihaela Mioara Mirea, Ionut Ivanescu 
Universitatea din Craiova, Romania 
Extensions of inequalities 
We discuss the extension of Jensen’s inequality on the right in ndimensional space. Jensen’s inequality is an important tool in convex analysis, revealing an essential feature of continuous convex functions.

Ioan Tincu 
"Lucian Blaga" University of Sibiu, Romania 
On a Markov method

This paper contains a new approch a transformed Markov method.

Mohsen Razzaghi 
Mississippi State University, USA 
An Efficient Technique for the Solution of
Fractional Ordinary Differential Equations

Fractional differential equations (FDEs) are generalizations of ordinary differential
equations to an arbitrary (noninteger) order. FDEs have attracted considerable
interest because of their ability to model complex phenomena. Due to the extensive
applications of FDEs in engineering and science, research in this area has grown significantly
all around the world. Generally speaking, most of the FDEs do not have
exact analytic solutions. Therefore, seeking numerical solutions of these equations
is becoming more and more important.
In this talk, an introduction to FDEs is given first. Then, an efficient numerical
method for solving the initial and boundaryvalue problems for FDEs is presented.
The method is based upon the fractional Taylor series approximations. The operational
matrix for the fractional Taylor series is given. This matrix is then utilized
to reduce the solution of the FDEs to a system of algebraic equations. We also
consider a specific equation known as BagletTorvik fractional differential equation.
This equation has an outstanding role in the modeling of several engineering
problems. The method is computationally very attractive and gives very accurate
results. The numerical solutions are compared with available exact or approximate
solutions in order to assess the accuracy of the proposed method.

Emil C. Popa 
"Lucian Blaga" University of Sibiu, Romania 
On a conditional inequality

In this paper we present some considerations on a conditional inequality.

Ioan Gavrea, Ivan Mircea 
Technical University of ClujNapoca, Romania 
Some asymptotic expansions of a sequence of Keller

We extend some known asymptotic expansions of a sequence attributed to Keller.

Manav Nesibe, Nurhayat Ispir 
Gazi University, Turkey 
Approxiantion by blending type operators based on LUPASSZÁSZ Functions

In this study, a certain bivariate summation integral type operators based on LupasSzász functions are introduced and investigated the degree of approximation. In terms of partial and total modulus of continuous and Kfunctional. Furtermore, the operators extended to Bögel continuous functions by the means of Generalized Boolean Approach.

Augusta Ratiu 
"Lucian Blaga" University of Sibiu, Romania 
A Refinement of Gruss Inequality

In this paper, we study the discrete
version of Gruss inequality, in the context of
elements of statistics, using the concepts of variance and
covariance for the random variables, obtaining a new refinement of this inequality.

Emilia Loredana Pop 
S.C. Light Soft S.R.L. ClujNapoca, Romania 
Scalar and Vector Optimization

Considering an optimization problem, the first approximated optimization problem and the dual optimization problem are attached to it and the connections between the optimal solutions and saddle points of these problems are studied.
In the vector case for the optimization problem and the first approximated optimization problem are studied the connections between the efficient solutions and saddle point for the Lagrangian of these two problems.

Beatrice Daniela Bucur 
Department of Computer Science, University of Pitesti, Romania 
Interpreting Modal Logics Using Labeled Graphs

Modal logic is an extension of the logic of predicates and propositions which
includes operators that express modality. In modal logic we deal with truth and falsehood
in different possible worlds, as well as in the real world. In this paper we construct a labeled
graph associated to a transition system, as a starting point in analyzing modal logics. We
define the concepts of inclusion, isomorphism, “modal equivalence” and equivalence between
graphs.

Adrian Gîrjoaba 
„Lucian Blaga” University of Sibiu, Romania 
Elliptic curves arising from an elementary problem

Starting from a problem regarding the Euler lines of some variable triangles
we get to a family of elliptic curves. This tells us that the solution can't come from
synthetic geometry. An analytical solution is presented, the computations being made with the aid of MAPLE.

Khan Khalid 
Jawaharlal Nehru University, Turkey 
Bezier curves based on Lupa\c{s} $(p,q)$analogue of Bernstein polynomials in CAGD

In this paper, we use the blending functions of Lupa\c{s} type (rational) $(p,q)$Bernstein operators based on $(p,q)$integers for construction of Lupa\c{s} $(p,q)$B$\acute{e}$zier curves (rational curves) and surfaces (rational surfaces) with shape parameters. We study the nature of degree elevation and degree reduction for Lupa\c{s} $(p,q)$B$\acute{e}$zier Bernstein functions. Parametric curves are represented using Lupa\c{s} $(p,q)$Bernstein basis.

Lopez Moreno Antonio Jesus 
University of Jaen, Spain 
TaylorDurrmeyer type operators

We present a sequence of linear positive operators of mixed TaylorDurrmeyer type. We study several approximation properties of these operators.

Adela Ionescu 
University of Craiova, Romania 
Optimal Control of a Stochastic Version for the Lotka  Volterra Model

We study a controlled dynamical system that reduces to the LotkaVolterra model of
competition between two species if the control variable is taken identically equal to 1.
Next, a transformation is used to simplify the dynamical system, and a stochastic version
of this transformed system is considered. The aim is to maximize the time that the ratio of
the number of individuals of each species remains between two acceptable limits, taking
the quadratic control costs into account. An explicit solution is found by solving the partial
differential equation satisfied by the value function.

Teodor Dumitru Valcan 
Babes  Bolyai University, Cluj  Napoca, Romania 
About a category of Abelian groups

We say that an Rmodule (abelian group) M has the direct summand intersection property (in short D.S.I.P.) if the intersection of any two direct summands of M is again a direct summand in M. In this work we will present three classes of abelian groups (torsion, divisible, respectively torsionfree) which have the property that any proper subgroup has D.S.I.P. and weare going to show that there are not such mixed groups.

Ali Aral 
Kirikkale University, Turkey 
On Quantiative Voronovkaya Type Theorems

.

Pandey Shikha 
Sardar Vallabhbhai National Institute of Technology, India 
Approximation properties of Chlodowsky variant of (p; q) BernsteinStancuSchurer operators

In the present paper, we introduce the Chlodowsky variant of (p; q) BernsteinStancuSchurer operators which is a generalization of (p; q) BernsteinStancuSchurer operators. We have also discussed its Korovkin type approximation properties and rate of convergence.

Çetin Nursel 
Turkish State Meteorological Service , Ankara, Turkey 


Kechagias Ioannis 
Technological Education Institute of Thessaly, Greece 


Tachev Gancho

University of Architecture, Sofia, Bulgaria 
Voronovskaja’s theorem for functions with
exponential growth

In the present Talk we establish general form of Voronovskaja’s theorem for functions defined on unbounded interval and having exponential growth. The case of aproximation by linear combinations is
also considered. Applications are given for some Sz´aszMirakyan and Baskakovtype operators.This talk is based on joint research with prof. Vijay Gupta

Paltanea Radu, Talpau Dimitriu Maria

Transilvania University of Brasov, Romania 
Moduli of continuity and related Kfunctionals 
We obtain echivalence theorems between certain moduli of continuity and Kfunctionals.

Agrawal Purshottam 
Indian Institute of Technology Roorkee,India 
Generalized boolen sum of linear positive operators 
Karl Bogel (1934,35) initiated the study of Bcontinuous and Bdifferentiable functions.
Badea and Cottin (1990) introduced the concept of GBS operators (Generalized Boolean Sum operators)
and proved an important "Test function theorem" (the analogue of the well known Korovkin theorem) for
the approximation of Bcontinuous functions by GBS operators. In the recent years, several researchers have contributed to this area of approximation theory. In the present talk, I propose to discuss these researches and the future scope of work.

Mioara Boncut 
"Lucian Blaga" University of Sibiu, Romania 
Dual Variational Principle for a Problem of Stationary Flow of a Viscuos Fluid 
In this paper we formulate the dual variational principle for a problem of stationary flow of a viscuos fluid in a pipe with omega transversal section in the Lform represented by a second elliptic equation with Dirichlet boundary conditions.

Dana Simian 
"Lucian Blaga" University of Sibiu, Romania 
Geometric Characterization of a Cubic Bezier Interpolation Scheme 
The aim of this paper is to provide a geometric characterization of a cubic B´ezier interpolation scheme. The interpolation points depend on two parameters t1, t2 ∈ (0, 1). Consequently we obtain a family of B´ezier interpolation curves depending on two parameters. Our characterization together with the associated algorithm realize a partition of the domain T = (0, 1) × (0, 1) where the parameters lie into regions corresponding to Bezier curves with zero, one or two inflexion points; with loop and with cusp. Computation, implementation of our interpolation scheme and graphic representations are made using MATLAB. 
