REFINING RECURSIVELY THE HERMITE-HADAMARD INEQUALITY ON A SIMPLEX

被引：6

作者：

Raissouli, Mustapha ^{[1
,2
]}

Dragomir, Sever S. ^{[3
,4
]}

机构：

[1] Taibah Univ, Fac Sci, Dept Math, Al Madinah Al Munawwarah 41477, Saudi Arabia

[2] Moulay Ismail Univ, Fac Sci, Dept Math, Meknes, Morocco

[3] Victoria Univ, Sch Sci & Engn, Res Grp Math Inequal & Applicat, Melbourne, Vic 8001, Australia

[4] Univ Witwatersrand, Sch Computat & Appl Math, ZA-2050 Johannesburg, South Africa

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2015年 / 92卷 / 01期

关键词：

convexity; simplex; Hermite-Hadamard inequality; refinement; convergence of recursive algorithms; CONVEX-FUNCTIONS; SIMPLICES;

D O I：

10.1017/S0004972715000258

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In the present paper, a coupled algorithm refining recursively the Hermite-Hadamard inequality on a simplex is investigated. Our approach allows us to express the integral mean value M-f of a convex function f on a simplex as both the limit of sequences and sum of series involving iterative lower and upper bounds of M-f. Two examples of interest are discussed.

引用

页码：57 / 67

页数：11

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