Positivity of Sums and Integrals for n-Convex Functions via Abel-Gontscharoff's Interpolating Polynomial and Green Functions

被引：0

作者：

Khan, Asif R. ^{[1
]}

Pecaric, Josip E. ^{[2
]}

Praljak, Marjan ^{[3
]}

Varosanec, Sanja ^{[4
]}

机构：

[1] Univ Karachi, Fac Sci, Dept Math, Univ Rd, Karachi 75270, Pakistan

[2] RUDN Univ, Miklukho Maklaya Str 6, Moscow 117198, Russia

[3] Univ Zagreb, Fac Food Technol & Biotechnol, Zagreb, Croatia

[4] Univ Zagreb, Dept Math, Zagreb 10000, Croatia

来源：

SOUTHEAST ASIAN BULLETIN OF MATHEMATICS | 2021年 / 45卷 / 02期

关键词：

n-convex functions; Abel-Gontscharoff's interpolating polynomial; Green function; Cebysev functional; INEQUALITY;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider positivity of sum Sigma(n)(i=1) p(i)f(x(i)) involving convex functions of higher order. Analogous for integral integral(b)(a) p(x)f(g(x))dx is also given. Representation of a function f via the Abel-Gontscharoff's Interpolating Polynomial and Green functions leads us to identities for which we obtain conditions for positivity of the mentioned sum and integral. We obtain bound for integral remainders which occur in those identities as well as corresponding mean value theorem.

引用

页码：197 / 216

页数：20

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Analele Stiintifice ale Universitatii Ovidius Constanta-Seria Matematica, 2016, 24 (03) :161-188

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