scholarly journals The Inequalities for Quasiarithmetic Means

2012 ◽  
Vol 2012 ◽  
pp. 1-25 ◽  
Author(s):  
Jadranka Mićić ◽  
Zlatko Pavić ◽  
Josip Pečarić
Keyword(s):  
Integral Functional ◽  
Power Means ◽  
Quasiarithmetic Means

Overview and refinements of the results are given for discrete, integral, functional and operator variants of inequalities for quasiarithmetic means. The general results are applied to further refinements of the power means. Jensen's inequalities have been systematically presented, from the older variants, to the most recent ones for the operators without operator convexity.

scholarly journals Refinements of Jensen’s Inequality via Majorization Results with Applications in the Information Theory

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Yongping Deng ◽  
Hidayat Ullah ◽  
Muhammad Adil Khan ◽  
Sajid Iqbal ◽  
Shanhe Wu
Keyword(s):  
Information Theory ◽  
Shannon Entropy ◽  
Probability Distributions ◽  
Jensen’S Inequality ◽  
Jensen Inequality ◽  
Jensen's Inequality ◽  
Power Means ◽  
Quasiarithmetic Means

In this study, we present some new refinements of the Jensen inequality with the help of majorization results. We use the concept of convexity along with the theory of majorization and obtain refinements of the Jensen inequality. Moreover, as consequences of the refined Jensen inequality, we derive some bounds for power means and quasiarithmetic means. Furthermore, as applications of the refined Jensen inequality, we give some bounds for divergences, Shannon entropy, and various distances associated with probability distributions.

scholarly journals Duality Theorems for (ρ,ψ,d)-Quasiinvex Multiobjective Optimization Problems with Interval-Valued Components

Mathematics ◽  
2021 ◽  
Vol 9 (8) ◽  
pp. 894
Author(s):  
Savin Treanţă
Keyword(s):  
Multiobjective Optimization ◽  
Optimization Problems ◽  
Integral Functional ◽  
Multiple Integral ◽  
Control Problems ◽  
Duality Theorems ◽  
New Class ◽  
Duality Results ◽  
Multiobjective Optimization Problems ◽  
Interval Valued

The present paper deals with a duality study associated with a new class of multiobjective optimization problems that include the interval-valued components of the ratio vector. More precisely, by using the new notion of (ρ,ψ,d)-quasiinvexity associated with an interval-valued multiple-integral functional, we formulate and prove weak, strong, and converse duality results for the considered class of variational control problems.

scholarly journals Generalized power means and interpolating inequalities

1999 ◽  
Vol 127 (1) ◽  
pp. 145-154 ◽  
Author(s):  
Hsu-Tung Ku ◽  
Mei-Chin Ku ◽  
Xin-Min Zhang
Keyword(s):  
Power Means

On the removability of a singularity for minimizers of an integral functional

2011 ◽  
Vol 56 (6) ◽  
pp. 493-501
Author(s):  
V. Cataldo ◽  
P. Cianci ◽  
S. D'Asero
Keyword(s):  
Integral Functional

The Study on Preventing Users Electic Larceny

2014 ◽  
Vol 602-605 ◽  
pp. 2939-2942
Author(s):  
Ying Ying Yang ◽  
Yi Shan ◽  
Zhi Tong Liu ◽  
Jian Feng Li ◽  
Jing Jin ◽  
...  
Keyword(s):  
Electric Power ◽  
Power Supply ◽  
Economic Loss ◽  
The Road ◽  
Energy Meter ◽  
Power Means ◽  
Long Time

For a long time,users electic larceny has been a headache topic of the electric power department.The users long-term electic larceny has brought great economic loss to the power supply department.In recent years,the stealing power means are emerging in an endless stream,and they have been broght mant difficulties to prevent electic larceny.But the road is high one feet evil spirite is high one a unit of lengh, according to the study on electic energy meter,we will understand the electic larceny means at the sours.Therefore, further study of stealing power means is also our current priority,only the better anti-stealing electic power means, can be completely blocked leak.

The reverse Hölder inequality for power means

2012 ◽  
Vol 183 (6) ◽  
pp. 762-771
Author(s):  
Viktor D. Didenko ◽  
Anatolii A. Korenovskyi
Keyword(s):  
Hölder Inequality ◽  
Reverse Hölder Inequality ◽  
Power Means ◽  
Reverse Hölder

scholarly journals Variational modelling of nematic elastomer foundations

2018 ◽  
Vol 28 (14) ◽  
pp. 2863-2904
Author(s):  
Pierluigi Cesana ◽  
Andrés A. León Baldelli
Keyword(s):  
Liquid Crystal ◽  
Integral Functional ◽  
Elastic Membrane ◽  
Two Dimensional ◽  
Order Tensor ◽  
Asymptotic Regime ◽  
Liquid Crystal Elastomer ◽  
Energy Functionals ◽  
Shear Energy ◽  
Dimensional Integral

We compute the [Formula: see text]-limit of energy functionals describing mechanical systems composed of a thin nematic liquid crystal elastomer sustaining a homogeneous and isotropic elastic membrane. We work in the regime of infinitesimal displacements and model the orientation of the liquid crystal according to the order tensor theories of both Frank and De Gennes. We describe the asymptotic regime by analysing a family of functionals parametrised by the vanishing thickness of the membranes and the ratio of the elastic constants, establishing that, in the limit, the system is represented by a two-dimensional integral functional interpreted as a linear membrane on top of a nematic active foundation involving an effective De Gennes optic tensor which allows for low order states. The latter can suppress shear energy by formation of microstructure as well as act as a pre-strain transmitted by the foundation to the overlying film.

Hölder-type inequalities for quasiarithmetic means

1986 ◽  
Vol 47 (3-4) ◽  
pp. 395-399 ◽  
Author(s):  
Zs. Páles
Keyword(s):  
Quasiarithmetic Means
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