Jensen-type inequalities for m-convex functions

被引：8

作者：

Bosch, Paul ^{[2
]}

Quintana, Yamilet ^{[3
]}

Rodriguez, Jose M. ^{[3
]}

Sigarreta, Jose M. ^{[1
]}

机构：

[1] Univ Autonoma Guerrero, Fac Matemat, Guerrero, Mexico

[2] Univ Desarrollo, Fac Ingn, Ave Plaza 680, Las Condes, Santiago De Chi, Chile

[3] Univ Carlos III Madrid, Dept Matemat, Ave Univ 30, Madrid 28911, Spain

来源：

OPEN MATHEMATICS | 2022年 / 20卷 / 01期

关键词：

Jensen-type inequalities; convex functions; m-convex functions; fractional derivatives and integrals; fractional integral inequalities; INTEGRAL-INEQUALITIES;

D O I：

10.1515/math-2022-0061

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays the main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work, we prove some new Jensen-type inequalities for m-convex functions and apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.

引用

页码：946 / 958

页数：13

共 31 条

[1]

[Anonymous], 1993, Fractional integrals and derivatives: theory and applications

[2]

Bakula M.K., 2008, J INEQ PURE APPL MAT, V7, P194

[3] Hermite-Hadamard-type inequalities for conformable integrals [J].

Bohner, Martin ;

Kashuri, Artion ;

Mohammed, Pshtiwan Othman ;

Napoles Valdes, Juan E. .

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS, 2022, 51 (03) :775-786

[4] Generalized inequalities involving fractional operators of the Riemann-Liouville type [J].

Bosch, Paul ;

Carmenate, Hector J. ;

Rodriguez, Jose M. ;

Sigarreta, Jose M. .

AIMS MATHEMATICS, 2022, 7 (01) :1470-1485

[5] ON MINKOWSKI AND HERMITE-HADAMARD INTEGRAL INEQUALITIES VIA FRACTIONAL INTEGRATION [J].

Dahmani, Zoubir .

ANNALS OF FUNCTIONAL ANALYSIS, 2010, 1 (01) :51-58

[6]

Dragomir S. S., 2000, Selected Topics on HermiteHadamard Type Inequalities

[7]

Dragomir S.S., 1993, Stud. Univ. Babes-Bolyai Math., V38, P21

[8] Hermite-Hadamard inequalities in fractional calculus defined using Mittag-Leffler kernels [J].

Fernandez, Arran ;

Mohammed, Pshtiwan .

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (10) :8414-8431

[9] Generalized fractional integral inequalities of Hermite-Hadamard-type for a convex function [J].

Han, Jiangfeng ;

Mohammed, Pshtiwan Othman ;

Zeng, Huidan .

OPEN MATHEMATICS, 2020, 18 :794-806

[10]

Izmailov P, 2018, UNCERTAINTY IN ARTIFICIAL INTELLIGENCE, P876

← 1 2 3 4 →