A new class of convex functions and applications in entropy and analysis

被引：1

作者：

Sayyari, Yamin ^{[1
]}

Dehghanian, Mehdi ^{[1
]}

机构：

[1] Sirjan Univ Technol, Dept Math, Sirjan, Iran

来源：

CHAOS SOLITONS & FRACTALS | 2024年 / 181卷

关键词：

Shannon's entropy; k-mean; k-harmonically convex function; Jensen's inequality; INEQUALITY;

D O I：

10.1016/j.chaos.2024.114677

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we introduce the concepts of ��-harmonic mean and ��-harmonically convex functions. As an application of ��-harmonic mean, we present a model in physics. Also, we prove Jensen type, Hermite- Hadamard type and Mercer type inequalities for these functions. Further, using this results, we give new bounds for Shannon entropy and geometrically mean.

引用

页数：6

共 50 条

[21] Hidden structures in the class of convex functions and a new duality transform
Artstein-Avidan, Shiri
Milman, Vitali
JOURNAL OF THE EUROPEAN MATHEMATICAL SOCIETY, 2011, 13 (04) : 975 - 1004
[22] Kolmogorov Entropy for Classes of Convex Functions
D. Dryanov
Constructive Approximation, 2009, 30 : 137 - 153
[23] On some class of convex functions
Sokol, Janusz
Nunokawa, Mamoru
COMPTES RENDUS MATHEMATIQUE, 2015, 353 (05) : 427 - 431
[24] On a Class of Convex Sets and Functions
Pierre Maréchal
Set-Valued Analysis, 2005, 13 : 197 - 212
[25] On a class of convex sets and functions
Maréchal, P
SET-VALUED ANALYSIS, 2005, 13 (02): : 197 - 212
[26] A RESTRICTED CLASS OF CONVEX FUNCTIONS
WOODS, CL
BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY, 1946, 52 (02) : 117 - 128
[27] Kolmogorov Entropy for Classes of Convex Functions
Dryanov, D.
CONSTRUCTIVE APPROXIMATION, 2009, 30 (01) : 137 - 153
[28] On stability of a class of convex functions
Korobkov, M
PROGRESS IN ANALYSIS, VOLS I AND II, 2003, : 207 - 213
[29] ON A CLASS OF PUNCTUAL CONVEX FUNCTIONS
Florea, Aurelia
Paltanea, Eugen
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2014, 17 (01): : 389 - 399
[30] The curse of dimensionality for the class of monotone functions and for the class of convex functions
Hinrichs, Aicke
Novak, Erich
Wozniakowski, Henryk
JOURNAL OF APPROXIMATION THEORY, 2011, 163 (08) : 955 - 965

← 1 2 3 4 5 →