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 Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness.

Radu Voichita Adriana, Acu Ana Maria

"Babes-Bolyai" University, Cluj-Napoca, Romania, "Lucian Blaga" University of Sibiu, Romania

About the iterates of some operators depending on a parameter

Muraru Carmen Violeta

"Vasile Alecsandri" University of Bacau, Romania

Some Approximation Properties of a Durrmeyer variant of q-Bernstein-Schurer Operators

Our goal is to present approximation theorems for a Durrmeyer variant of q-Bernstein-Schurer 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 q-Bernstein-Schurer 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 q-Bernstein- Schurer operators.

Naokant Deo

Delhi Technological University (Formerly Delhi College of Engineering), India

Modified Durrmeyer Operators Based On Inverse Polya-Eggenberger Distribution

In this contribution we consider modified Durrmeyer operators associated to inverse P\' olya-Eggenberger 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 Kantorovich-type 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

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Alina Babos

"Nicolae Balcescu " Land Forces Academy, Sibiu, Romania

Interpolation operators on a square with one curved side

We construct some Lagrange, Hermite and Birkhoff-type 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.

Bascanbaz-Tunca Gülen,

Ayşegül Erençin, Fatma Taşdelen

Ankara University, Turkey

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 Lucas-balancing numbers

In this paper, we present new congruences involving balancing and cobalancing numbers.

Gavrea Bogdan

Technical University of Cluj-Napoca, Romania

Stochastic complementarity problems for a class of rigid body systems

We consider a class of rigid body systems in a quasi-static 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 F-G-contraction 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 Max-Product Kind

In this study, we present the nonlinear generalized Szász operators of max-product 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 Korovkin-type 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 Stancu-Chlodowsky polynomials. We made a comparison between the approximations obtained by the generalized Bernstein operator and the Stancu-Chlodowsky 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

Bi-criteria problems for energy optimization

In this material we consider a new approach for energy optimization based on bi-criteria 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 Jakimovski-Leviatan-Durrmeyer type operators

In this paper we introduce the Chlodowsky variant of the Durrmeyer-type Jakimovsky Leviatan operators. We give the rate of approximation in terms of first order modulus of continuity and the Ditzian-Totik modulus of smoothness. Also we introduce a Voronovskaja-type asymptotic formula. In the last section we give some approximation results for a weighted space.

P.N. Agrawal

Indian Institute of Technology Roorkee,India

Bernstein-Schurer-Kantorovich operators based on (p,q)-integers

The purpose of the present paper is to introduce the (p, q)-analogue of Bernstein-Schurer-Kantorovich 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)-Bernstein-Schurer-Kantorovich 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 vis-a-vis Bernstein-Schurer and Bernstein-Kantorovich operators based on (p, q)-integers.

Adonia-Augustina Opris

Technical University of Cluj-Napoca, 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 q-Bleimann, Butzer and Hahn Operators

In this work, we consider a generalization of the sequences of q-Bleimann, 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

p-extending Modules with Abelian Endomorphism Rings

A module M is called p-extending if every projection invariant submodule of M is essential in a direct summand of M. We focus our attention on p-extending 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 Economics-Varna, 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 Ciobotariu-Boer

"Avram Iancu" High School, Cluj-Napoca, 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 Calin-Ioan

Romanian Academy, "T. Popoviciu" Institute of Numerical Analysis, Cluj-Napoca, 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 1933-1934). 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 Sturm-Liouville eigenvalue problem.

Tercan Adnan

Hacettepe University, Turkey

p-extending 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 n-dimensional 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 boundary-value 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 Baglet-Torvik 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 Cluj-Napoca, 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 LUPAS-SZÁSZ Functions

In this study, a certain bivariate summation integral type operators based on Lupas-Szász functions are introduced and investigated the degree of approximation. In terms of partial and total modulus of continuous and K-functional. 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. Cluj-Napoca, 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

Taylor-Durrmeyer type operators

We present a sequence of linear positive operators of mixed Taylor-Durrmeyer 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 Lotka-Volterra 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 R-module (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 torsion-free) 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

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Pandey Shikha

Sardar Vallabhbhai National Institute of Technology, India

Approximation properties of Chlodowsky variant of (p; q) Bernstein-Stancu-Schurer operators

In the present paper, we introduce the Chlodowsky variant of (p; q) Bernstein-Stancu-Schurer operators which is a generalization of (p; q) Bernstein-Stancu-Schurer 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´asz-Mirakyan and Baskakov-type 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 K-functionals

We obtain echivalence theorems between certain moduli of continuity and K-functionals.

Agrawal Purshottam

Indian Institute of Technology Roorkee,India

Generalized boolen sum of linear positive operators

Karl Bogel (1934,35) initiated the study of B-continuous and B-differentiable 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 B-continuous 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 L-form represented by a second elliptic equation with Dirichlet boundary conditions.