Dear participants,

Unfortunately, because of some technical problems some registrations to ICATA 2022 were not received.

If your name does not appear in the list of participants, please send the abstract of your talk to the email address: anamaria.acu@ulbsibiu.ro

Once more, please, accept our sincere apologies.

Plenary Speakers

Ioan Rasa, Technical University of Cluj-Napoca, Romania

Francesco Altomare, University of Bari, Italy

Gianluca Vinti, University of Perugia, Italy

Stefano De Marchi, University of Padua, Italy

Participants

Name Institution Title Abstract
Francesco Altomare
Department of Mathematics, University of Bari
Approximation processes and representation formulae for operator semigroups in terms of integrated means
The representation/approximation formulae for strongly continuous operator semigroups (in short, C0 - semigroups) are of interest both from a theoretical point of view and from an applied one, especially when they are involved, for instance, in the numerical analysis of the partial differential equations governed by such C0 -semigroups. Various methods and results are known in this field, often accompanied by a through study of the rate of convergence of the given representations/approximations. The talk will be devoted to report some recent results on such a topic which are documented in the paper [1] and which has been jointly written with M. Cappelletti Montano and V. Leonessa. Of concern are some representation formulae for C0 -semigroups on Banach spaces, in terms of integrated means with respect to a given family of probability Borel measures and other parameters. Such representation formulae have been suggested by some recent studies devoted to new sequences of positive linear operators which, among other things, generalize both Bernstein operators as well as Kantorovich operators ([2], [3]). They extend the representation formulae which have been obtained in [4] with purely probabilistic methods. Some estimates of the rate of convergence in terms of the rectified modulus of continuity and the second modulus of continuity will be discussed as well.
Stefano De Marchi
Dipartimento di Matematica "Tullio Levi-Civita", University of Padova (UNIPD), Italy
(\beta,\gamma)-Chebyshev functions and points of the interval and some extensions
In this talk, we introduce the class of (\beta,\gamma)-Chebyshev functions and corresponding points, which can be seen as a family of generalized Chebyshev polynomials and points. For the (\beta,\gamma)-Chebyshev functions, we prove that they are orthogonal in certain subintervals of [-1,1] with respect to a weighted arc-cosine measure. In particular we investigate the cases where they become polynomials, deriving new results concerning classical Chebyshev polynomials of first kind. Besides, we show that subsets of Chebyshev and Chebyshev-Lobatto points are instances of (\beta,\gamma)-Chebyshev points. We also study the behavior of the Lebesgue constants of the polynomial interpolant at these points on varying the parameters (\beta) and (\gamma). If time allows, we discuss their extension to the square [-1,1]^2. This is a joint work with Giacomo Elefante and Francesco Marchetti (both from UNIPD).
"Vasile Alecsandri" University of Bacau
Recently, the idea of exponential type operators is extended in capturing semi-exponential operators as generalization of the first ones. The present study is focused on the approximation properties of the semi-exponential Baskakov operators type, connected with . A Voronovskaja type results are obtained and some approximation properties in the weighted spaces of continuous functions are also studied.
George Popescu
University of Craiova, Department of Applied Mathematics
Rhaly Operators, Boundedness, Compactness, Zero Statistical Density
We present a study upon Rhaly operators on Hilbert spaces, that is operators defined by "terraced matrices". We prove a necessary condition for a terraced matrix to define a bounded Rhaly operator, or a compact operator, involving subsequences with zero statistical density. We show that boundedness and compactness of Rhaly operators are reduced to study the Rhaly operators defined by subsequences of the reciprocal of natural numbers. This leads to study the reduced operators of the Cesaro operator and investigate harmonic series defined by subsequences of natural numbers with zero statistical density.
Ioan Rasa (joint work with Ana Maria Acu)
Technical University of Cluj-Napoca
Analytic inequalities and stochastic orders
The talk is devoted to a family of analytic inequalities connected with positive linear operators and stochastic orders. The results are formulated in analytic terms and/or probabilistic terms.
Nicusor Minculete
Transilvania University of Brasov
Several inequalities related the numerical radius
The aim of this presentation is to give new upper bounds of \omega(T), which denotes the numerical radius of an operator T on a Hilbert space (H,\langle\cdot,\cdot\rangle). Next, we give certain inequalities about radius \omega(S^*T).
Ariana Pitea
University Politehnica of Bucharest
Numerical reckoning of fixed points in a geometric framework
Numerical schemes for the reckoning of fixed points with adequate properties are presented, regarding three step independent iterative procedures. Convergence results are established. A qualitative study is made, from the point of view of T-stability and data dependence.
Diana Curila (Popescu) (joint work with Alexandru Mihai Bica)
University of Oradea, Department of Mathematics and Informatics
The Akima.s Fitting Method for Quartic Splines
For the Hermite type quartic spline interpolating on the partition knots and at the midpoint of each subinterval, we consider the estimation of the derivatives on the knots, and the values of these derivatives are obtained by constructing an algorithm of Akima.s type. For computing the derivatives on end-points are also considered alternatives that request optimal properties near the end-points. The error estimate in the interpolation with this quartic spline is generally obtained in terms of the modulus of continuity. In the case of interpolating smooth functions, the corresponding error estimate reveal the maximal order of approximation O(h3). A numerical experiment is presented for making the comparison between the Akima.s cubic spline and the Akima.s variant quartic spline having de.ciency 2 and natural end-point conditions.
Zoltan Satmari (joint work with Alexandru Mihai Bica)
University of Oradea, Department of Mathematics and Informatics
Bernstein numerical method for solving nonlinear fractional and weakly singular Volterra integral equations of the second kind
We will show a method of approximation for a fractional nonlinear Volterra integral equation. This method is based on Banach's Fixed Point Theorem. At each iteration step of this method, we will apply a Bernstein polynomial approximation of the functions involved in the integral. At the end of the article, we will demonstrate our results, providing some numerical examples.
Ioan Cristian Buscu, Ancuta Emilia Steopoaie
Technical University, Cluj-Napoca
Voronovskaja type results for generalized Baskakov operators preserving monomials
We consider generalized Baskakov operators preserving the constant function 1 and a monomial x^j. For them we establish Voronovskaja type results.
Ioan Cristian Buscu, Andra Mihaela Seserman
Technical University, Cluj-Napoca
Convergence of special sequences of positive operators
Some modified sequences of positive linear operators converge to other positive linear operators. We present a general result in this direction and illustrate it by several examples.
Irina Savu
University Politehnica of Bucharest
Orbital Fuzzy Iterated Function Systems
In this paper we introduce the concept of orbital fuzzy iterated function system and prove that the fuzzy operator associated to such a system is weakly Picard. An example is provided.
Marta Enachioiu, Gabriela Denisa Motronea
Technical University, Cluj-Napoca
Positive solutions of algebraic systems with positive coefficients
We consider a special family of nonlinear algebraic systems of equations with positive coefficients and investigate the existence of positive solutions. The uniqueness of a positive solution is also studied.
Benaissa Zerroudi
Faculty of science, Ibn Zohr University - Agadir
Enhancing the approximation order of Shepherd operators through barycentric coordinates
This paper presents a new approach to constructing approximation operators, with cubic and quartic approximation order, which interpolates functional values on a set of scattered data. We based on a combination of multinodes Shepard basis functions with rational interpolants based on set of nodes. Numerical results show the efficiency and accuracy of the proposed operators and are implemented by fast algorithms that are useful in multiple applications.
Ionut Tudor Iancu
University of Oradea, Department of Mathematics and Computer Science
Statistical convergence in a Korovkin-type theorem for monotone and sublinear operators
In this paper we generalize the result on statistical uniform convergence in the Korovkin theorem for positive and linear operators in C([a, b]), to the more general case of monotone and sublinear operators. Our result is illustrated by concrete examples.
Daniela Inoan, Daniela Marian
Department of Mathematics, Technical University of Cluj-Napoca
Semi-Hyers-Ulam-Rassias Stability of a Volterra Integro-Differential Equation with a Convolution Type Kernel via Laplace Transform
We present some results regarding semi-Hyers-Ulam-Rassias stability of a Volterra integro-differential equation of order I, II and n, with a convolution type kernel. To this purpose the Laplace transform is used. The results obtained show that the stability holds for problems formulated with various functions: exponential and polynomial functions.
Transilvania University of Brasov
On a method for uniform summation of the Fourier-Jacobi series
We point out that there is a matrix method of summation of Fourier-Jacobi series attached to all continuous functions, which is given by the representation of Durrmeyer operators with Jacobi weight. It is shown that this method of summation is stronger than the Cesaro methods of summation of all orders.
Miruna-Stefana Sorea
Lucian Blaga University of Sibiu
Poincare-Reeb graphs of real algebraic domains
An algebraic domain is a closed topological subsurface of a real affine plane whose boundary consists of disjoint smooth connected components of real algebraic plane curves. We study the non-convexity of an algebraic domain by collapsing all vertical segments contained in it: this yields a Poincare-Reeb graph, which is naturally transversal to the foliation by vertical lines. Using an adapted version of a Weierstrass-type approximation theorem, we show that any transversal graph whose vertices have only valencies 1 and 3 and are situated on distinct vertical lines can be realized as a Poincaré-Reeb graph. This talk is based on joint work with Arnaud Bodin and Patrick Popescu-Pampu.
Universitatea Lucian Blaga din Sibiu
On the log-convexity of a Bernstein-like polynomials sequence
We prove that the sequence of the sum of the squares of the Bernstein polynomials is log-convex. There are given two proofs of this result: one by relating our sequence to the Legendre polynomials sequence and one by induction. I know of this problem from Professor Ioan Rasa, Cluj-Napoca.
Gabriel Prajitura, Andrei Vernescu
State University of New York, United States; Valahia University of Târgovi?te (retired) Romania
About uniform continuous functions which are not Lipschitz
To approximate a function, some simpler functions are used: simpler as definitory structure (formula) and also as regularity, continuity and/or smoothness. Any Lipschitz function is a uniformly continuous function, but conversely it not always true. We add to the usual examples some other, especially of the class of differentiable functions.
Andra Malina
Babes-Bolyai University of Cluj-Napoca, Romania
Univariate Shepard operators combined with least squares fitting polynomials
We construct three new univariate Shepard operators using linear, quadratic and cubic polynomials in order to improve the approximation results of the Shepard method. The polynomials are constructed such that they fit the interpolation data in a weighted least squares approximation way.
Alexandru-Mihai Bica
Catmul-Rom quartic splines
The quartic degree variant of Catmul-Rom splines that interpolates on mesh points and at midpoints is defined. The error estimates are obtained providing the optimal order of convergence O(h^5). The usefulness of these splines for the numerical solution of two-point boundary value problems, associated to fifth order functional differential equations, is pointed out.
Doru Dumitrescu
University Politehnica Bucharest, Romania
Fixed point results on Jleli-Samet metric spaces
In the setting of Jleli-Samet metric spaces, existence and uniqueness fixed point theorems are stated and proved. We used generalized contractive operators obtained as a sum of mappings with adequate properties. As consequences, some classic results in literature are obtained.
Gülen Bascanbaz-Tunca
Ankara University, Turkey
Generalized Kantorovich Operators on Multidimensional Hypercube
In this talk, based on the construction of Stancu's operators [1], we introduce a new generalization of Kantorovich operators acting on $L^p( Q)$, $1\leq p<\infty$, where $Q$ is a multidimensional unit hypercube. We study approximation in $L^p$-norm by the sequence of such operators. And, for the rate of the approximation, we present some estimates via multivariate averaged modulus of smoothness of the first order for functions from $L^p( Q)$ as well as from a smooth subspace of $L^p( Q)$.
Jose A. Adell and Daniel Cardenas-Morales (speaker)
University of Zaragoza and University of Ja\'{e}n, Spain
On the constant in a direct inequality for the Szasz-Mirakyan operator
We are concerned with the approximation of continuous functions by the classical Sz\'{a}sz-Mirakyan operators $S_t$, $t>1$, in terms of the Ditzian-Totik modulus of smoothness $\omega_2^{\varphi}$ with step-weight function $\varphi (x)=\sqrt{x}$. Information about the rate of uniform convergence is given by the direct inequality $$\|S_tf-f\|_{[0,\infty )}\leq K_S\omega_2^{\varphi}\left(f;\frac{1}{\sqrt{t}}\right).$$ Here, we focus on the absolute constant $K_S$, and prove that it can be taken smaller than $2.5$.
Gianluca Vinti
University of Perugia, Italy
A mathematical model for the study of vascular patologies
I will present a mathematical model based on the study of some sampling type operators whose approximation results lead to applications to the reconstruction and the enhancement of digital images. These, in turn, will allow to solve a diagnostic problem, concerning vascular pathologies, studied within the CARE project.
Mirella Cappelletti Montano (joint work with Benedetta Lisena)
Università degli Studi di Bari Aldo Moro, Italy
A diffusive two predators-one prey model on periodically evolving domains
The talk deals with a diffusive two predators-one prey model with Holling-type II functional response. We assume that the density of prey and predators are spatially inhomogeneous on a (periodically) evolving domain and are subject to homogeneous Neumann boundary conditions. We study the asymptotic properties of the solutions of this reaction-diffusion model. More specifically, we introduce suitable conditions in order that one predator species faces extinction and the surviving predator and its prey coexist stably, showing that their density, as time increases, tends to the periodic solution of the corresponding kinetic two species predator-prey model. We also consider an autonomous model on a fixed domain.
Marius-Mihai Birou
Technical University of Cluj Napoca
New bounds for the complete elliptic integral of the first kind
The complete elliptic integral of the first kind has applications in mathematics, physics and engineering. A lot of researchers has attracted to obtain inequalities for this integral. In this article we give new bounds for the complete elliptic integral of the first kind.
Alina Ramona Baias
Technical University of Cluj Napoca
On the Best Ulam constant of some linear difference equations
Abstract: An equation is called Ulam stable if for every approximate solution of it there exists an exact solution near it. In this talk, we present some stability results for the $p$ order linear difference equation with constant coefficients $$x_{n+p}=a_1x_{n+p-1}+\ldots+a_px_n.$$ For some particular cases the Best Ulam constant is also obtained.