Page 134 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 134
APPROXIMATION THEORY AND APPLICATIONS (MS-78)
Modification of exponential type operators preserving exponential
functions connected with x3
Carmen Violeta Popescu (Muraru), carmen 7419@yahoo.com
Vasile Alecsandri University of Bacau, Romania
Coauthors: Ali Aral, Vijay Gupta
In the present paper, we propose modification of the exponential type operators, which are
connected with x3. Such operators are connected with exponential functions. We estimate
moments and establish some direct results in terms of modulus of continuity.
A Hermite-Hadamard type inequality with applications to the estimation
of moments of convex functions of random variables
Pas, ca Raluca Ioana, raluca.pasca24@yahoo.com
Technical University Cluj-Napoca, Romania
Coauthor: Gavrea Bogdan
In this paper we present a Hermite-Hadamard type inequality with applications to the estima-
tion of moments for convex functions of several random variables. A particular case of the
derived result can be applied to estimate the sum of moments for identically distributed random
variables. We were motivated in our research by the applications of moment estimation in fields
such as probability theory, mathematical statistics and statistical learning.
Information potential for some probability distributions
Ioan Rasa, ioan.rasa@math.utcluj.ro
Technical University of Cluj-Napoca, Romania
Coauthor: Ana Maria Acu
This talk is devoted to some properties of the entropies of some discrete or continuous probabil-
ity distributions. We will focus on the information potential (IP) associated with such distribu-
tions depending on a real parameter x. The Rényi entropy and the Tsallis entropy are naturally
related to IP. Convexity properties and bounds of the associated IP, useful in Information Theo-
retic Learning, are discussed and translated as properties of the entropies. Several examples and
numerical computations illustrate the general results as well as their relationship with positive
linear operators.
Bounds for Several Statistical Indicators
Augusta Ratiu, augusta.ratiu@ulbsibiu.ro
Lucian Blaga University of Sibiu, Romania
In this paper, we study the problem of finding new bounds for some statistical indicators that
characterize a data series. Using a refinement of Aczél’s inequality, we find other bounds for
dispersion, standard deviation and coefficient of variation.
132
Modification of exponential type operators preserving exponential
functions connected with x3
Carmen Violeta Popescu (Muraru), carmen 7419@yahoo.com
Vasile Alecsandri University of Bacau, Romania
Coauthors: Ali Aral, Vijay Gupta
In the present paper, we propose modification of the exponential type operators, which are
connected with x3. Such operators are connected with exponential functions. We estimate
moments and establish some direct results in terms of modulus of continuity.
A Hermite-Hadamard type inequality with applications to the estimation
of moments of convex functions of random variables
Pas, ca Raluca Ioana, raluca.pasca24@yahoo.com
Technical University Cluj-Napoca, Romania
Coauthor: Gavrea Bogdan
In this paper we present a Hermite-Hadamard type inequality with applications to the estima-
tion of moments for convex functions of several random variables. A particular case of the
derived result can be applied to estimate the sum of moments for identically distributed random
variables. We were motivated in our research by the applications of moment estimation in fields
such as probability theory, mathematical statistics and statistical learning.
Information potential for some probability distributions
Ioan Rasa, ioan.rasa@math.utcluj.ro
Technical University of Cluj-Napoca, Romania
Coauthor: Ana Maria Acu
This talk is devoted to some properties of the entropies of some discrete or continuous probabil-
ity distributions. We will focus on the information potential (IP) associated with such distribu-
tions depending on a real parameter x. The Rényi entropy and the Tsallis entropy are naturally
related to IP. Convexity properties and bounds of the associated IP, useful in Information Theo-
retic Learning, are discussed and translated as properties of the entropies. Several examples and
numerical computations illustrate the general results as well as their relationship with positive
linear operators.
Bounds for Several Statistical Indicators
Augusta Ratiu, augusta.ratiu@ulbsibiu.ro
Lucian Blaga University of Sibiu, Romania
In this paper, we study the problem of finding new bounds for some statistical indicators that
characterize a data series. Using a refinement of Aczél’s inequality, we find other bounds for
dispersion, standard deviation and coefficient of variation.
132
