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Plenary Speakers

Agrawal Purshottam (Indian Institute of Technology Roorkee, India)

Vijay Gupta (Department of Mathematics, Netaji Subhas Institute of Technology, India)

Octavian Agratini ("Babes Bolyai" University, Cluj-Napoca, Romania)

Ali Aral (Kirikkale University, Turkey)

Mohammad Mursaleen (Aligarh Muslim University, India)

Mohsen Razzaghi (Mississippi State University, USA)

Toma Albu (Institute of Mathematics of the Romanian Academy)

Participants
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 Ditzian-Totik modulus of smoothness and a Voronovskaja type theorem by using the Ditzian-Totik modulus of smoothness.
"Babes-Bolyai" University, Cluj-Napoca, Romania, "Lucian Blaga" University of Sibiu, Romania
About the iterates of some operators depending on a parameter
During the last decade, q-Calculus 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 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

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 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.
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.
"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
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.
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.
„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.
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