GENERALIZATION OF JENSEN'S INEQUALITY BY LIDSTONE'S POLYNOMIAL AND RELATED RESULTS

被引：16

作者：

Aras-Gazic, Gorana ^{[1
]}

Culjak, Vera ^{[2
]}

Pecaric, Josip ^{[3
,4
]}

Vukelic, Ana ^{[5
]}

机构：

[1] High Sch Jelkovec, Sesvete 10360, Croatia

[2] Univ Zagreb, Fac Civil Engn, Dept Math, Zagreb 10000, Croatia

[3] GC Univ, Abdus Salam Sch Math Sci, Lahore Gulberg 54660, Pakistan

[4] Univ Zagreb, Fac Text Technol, Zagreb 10000, Croatia

[5] Univ Zagreb, Dept Math, Fac Food Technol & Biotechnol, Zagreb 10000, Croatia

来源：

MATHEMATICAL INEQUALITIES & APPLICATIONS | 2013年 / 16卷 / 04期

关键词：

Green function; Jensen inequality; (2n)-convex function; completely convex function; Lidstone polynomial; Cauchy type mean value theorems; n-exponential convexity; exponential convexity; log-convexity; means; CONVEX-FUNCTIONS; ANALYTIC-FUNCTIONS; HIGHER-ORDER; SERIES;

D O I：

10.7153/mia-16-96

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we consider (2n)-convex functions and completely convex functions. Using Lidstone's interpolating polynomials and conditions on Green's functions we present results for Jensen's inequality and converses of Jensen's inequality for signed measure. By using the obtained inequalities, we produce new exponentially convex functions. Finally, we give several examples of the families of functions for which the obtained results can be applied.

引用

页码：1243 / 1267

页数：25

共 20 条

[1]

AGARWAL R. P., 1993, Error Inequalities in Polynomial Interpolation and Their Applications

[2]

[Anonymous], 1992, Math. Sci. Eng

[3]

Atkinson KE., 1989, INTRO NUMERICAL ANAL

[4] The definition and properties of analytic functions of a real variable [J].