EXPONENTIAL TRIGONOMETRIC CONVEX FUNCTIONS AND HERMITE-HADAMARD TYPE INEQUALITIES

被引：29

作者：

Kadakal, Mahir ^{[1
]}

Iscan, Imdat ^{[1
]}

Agarwal, Praveen ^{[2
,3
,4
,5
]}

Jleli, Mohamed ^{[6
]}

机构：

[1] Giresun Univ, Sci & Arts Fac, Dept Math, TR-28200 Giresun, Turkey

[2] Anand Int Coll Engn, Dept Math, Jaipur 303012, Rajasthan, India

[3] Harish Chandra Res Inst, Rajasthan Dept Math, Allahabad 211019, Uttar Pradesh, India

[4] Int Ctr Basic & Appl Sci, Jaipur 302029, Rajasthan, India

[5] Inst Math & Math Modeling, Alma Ata, Kazakhstan

[6] King Saud Univ, Coll Sci, Dept Math, Riyadh, Saudi Arabia

来源：

MATHEMATICA SLOVACA | 2021年 / 71卷 / 01期

关键词：

Convex function; trigonometric convex function; exponential trigonometric convex functions; Hermite-Hadamard inequality; Holder-Iscan inequality; improved power-mean inequality;

D O I：

10.1515/ms-2017-0410

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Holder-Iscan and improved power-mean integral inequalities give better approximations than that obtained with Holder and improved power-mean integral inequalities.

引用

页码：43 / 56

页数：14

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