Popoviciu type inequalities via Green function and Taylor polynomial

被引：8

作者：

Butt, Saad Ihsan ^{[1
]}

Khan, Khuram Ali ^{[2
]}

Pecaric, Josip ^{[3
]}

机构：

[1] COMSATS, Inst Informat Technol, Dept Math, Lahore, Pakistan

[2] Univ Sargodha, Dept Math, Sargodha, Pakistan

[3] Univ Zagreb, Fac Text Technol, Zagreb, Croatia

来源：

TURKISH JOURNAL OF MATHEMATICS | 2016年 / 40卷 / 02期

关键词：

Popoviciu inequality; Taylor formula; Green function; Cebysev functional; Gruss inequality; Ostrowski inequality; exponential convexity; Cauchy mean;

D O I：

10.3906/mat-1501-38

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The well-known Taylor polynomial is used to construct the identities coming from Popoviciu type inequalities for convex functions via the Green function. The bounds for the new identities are found using the Cebysev functional to develop the Grass and Ostrowski type inequalities. Further, more exponential convexity together with Cauchy means is presented for linear functionals associated with the obtained inequalities.

引用

页码：333 / 349

页数：17

共 13 条

[1]

Bernstein S, 1929, ACTA MATH-DJURSHOLM, V52, P1

[2] SOME NEW OSTROWSKI-TYPE BOUNDS FOR THE CEBYSEV FUNCTIONAL AND APPLICATIONS [J].

Cerone, P. ;

Dragomir, S. S. .

JOURNAL OF MATHEMATICAL INEQUALITIES, 2014, 8 (01) :159-170

[3]

HORVATH L., 2014, Monographs in Inequalities, V8

[4]

Jaksetic J, 2013, J CONVEX ANAL, V20, P181

[5] Steffensen inequality, higher order convexity and exponential convexity [J].

Jaksetic, Julije ;

Pecaric, Josip ;

Perusic, Anamarija .

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO, 2014, 63 (01) :109-127

[6]

Khan K. A., 2014, J MATH COMPUT SCI, V4, P1091

[7] Differences of Weighted Mixed Symmetric Means and Related Results [J].

Khan, Khuram Ali ;

Pecaric, J. ;

Peric, I. .

JOURNAL OF INEQUALITIES AND APPLICATIONS, 2010,

[8]

Niculescu CP, 2009, J MATH INEQUAL, V3, P323

[9]

Niculescu CP., 2006, Bull. Math. Soc. Sci. Math. Roumanie (N.S.), V49, P285

[10]

Pecaric J., 1992, Mathematics in Science and Engineering

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