Multidimensional generalization of the Korous inequality

2016 ◽  
Vol 27 (5) ◽  
pp. 405-412
Author(s):  
B. Ftorek ◽  
P. Oršanský ◽  
H. Šamajová
Keyword(s):  
Multidimensional Generalization

scholarly journals Preserving the Shape of Functions by Applying Multidimensional Schoenberg-Type Operators

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1016
Author(s):  
Camelia Liliana Moldovan ◽  
Radu Păltănea
Keyword(s):  
Applied Sciences ◽  
Degree Of Approximation ◽  
Higher Order ◽  
Second Order ◽  
Dimensional Case ◽  
Moduli Of Continuity ◽  
One Dimensional ◽  
Multidimensional Generalization ◽  
The One

The paper presents a multidimensional generalization of the Schoenberg operators of higher order. The new operators are powerful tools that can be used for approximation processes in many fields of applied sciences. The construction of these operators uses a symmetry regarding the domain of definition. The degree of approximation by sequences of such operators is given in terms of the first and the second order moduli of continuity. Extending certain results obtained by Marsden in the one-dimensional case, the property of preservation of monotonicity and convexity is proved.

scholarly journals On the convergence of multidimensional regular C-fractions with independent variables

2018 ◽  
Vol 26 (1) ◽  
pp. 18 ◽  
Author(s):  
R.I. Dmytryshyn
Keyword(s):  
Power Series ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Open Disk ◽  
Efficient Tool ◽  
Independent Variables ◽  
Multidimensional Generalization ◽  
Multiple Power ◽  
Multiple Power Series ◽  
Branched Continued Fraction

In this paper, we investigate the convergence of multidimensional regular С-fractions with independent variables, which are a multidimensional generalization of regular С-fractions. These branched continued fractions are an efficient tool for the approximation of multivariable functions, which are represented by formal multiple power series. We have shown that the intersection of the interior of the parabola and the open disk is the domain of convergence of a multidimensional regular С-fraction with independent variables. And, in addition, we have shown that the interior of the parabola is the domain of convergence of a branched continued fraction, which is reciprocal to the multidimensional regular С-fraction with independent variables.

Multidimensional reversed Hardy type inequalities for monotone functions

2014 ◽  
Vol 07 (04) ◽  
pp. 1450055
Author(s):  
Saad Ihsan Butt ◽  
Josip Pečarić ◽  
Ivan Perić ◽  
Marjan Praljak
Keyword(s):  
Mean Value ◽  
Monotone Functions ◽  
Mean Value Theorems ◽  
Hardy Type Inequalities ◽  
Multidimensional Generalization ◽  
Exponential Convexity ◽  
Hardy Type ◽  
Cauchy Means

In this paper, we will give some multidimensional generalization of reversed Hardy type inequalities for monotone functions. Moreover, we will give n-exponential convexity, exponential convexity and related results for some functionals obtained from the differences of these inequalities. At the end we will give mean value theorems and Cauchy means for these functionals.

Sign in / Sign up

Export Citation Format

Share Document