SOME INEQUALITIES FOR WEIGHTED AND INTEGRAL MEANS OF CONVEX FUNCTIONS ON LINEAR SPACES

被引：0

作者：

Dragomir, Silvestru Sever ^{[1
,2
]}

机构：

[1] Victoria Univ, Coll Engn & Sci, Math, POB 14428, Melbourne, Vic 8001, Australia

[2] Univ Witwatersrand, DST NRF Ctr Excellence Math & Stat Sci, Sch Comp Sci & Appl Math, Private Bag 3, ZA-2050 Johannesburg, South Africa

来源：

PROCEEDINGS OF THE INSTITUTE OF MATHEMATICS AND MECHANICS | 2020年 / 46卷 / 02期

关键词：

Convex functions; Linear spaces; Integral inequalities; Hermite-Hadamard inequality; Fejer's inequalities; Norms and semi-inner products; OSTROWSKI TYPE;

D O I：

10.29228/proc.29

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let f be a convex function on a convex subset C of a linear space and x, y is an element of C, with x not equal y. If p : [0, 1] -> R is a Lebesgue integrable and symmetric function, namely p (1 - t) = p (t) for all t is an element of [0, 1] and such that the condition 0 <= integral(tau)(0) p(s) ds <= integral(1)(0) p(s) ds for all tau is an element of [0, 1] holds, the we have vertical bar 1/integral(1)(0) p(tau)d tau integral(1)(0) p(tau) f ((1 - tau)x + tau y)d tau - integral(1)(0)f((1 - tau)x + tau y)d tau vertical bar <= 1/integral(1)(0)p(tau) d tau integral(1)(0)(integral(tau)(0)p(s) ds) (1- tau)d tau [del( -) f(y) (y - x) -del (+) f(x) (y - x)] <= 1/2 [del (-)f(y) (y - x) - del(+) f(x) (y - x)]. Some applications for norms and semi-inner products are also provided.

引用

页码：197 / 209

页数：13

共 11 条

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