Generalization of Popoviciu-Type Inequalities Via Fink’s Identity

被引：0
作者：
Saad Ihsan Butt
Josip Pečarić
Ana Vukelić
机构：
[1] COMSATS,Department of Mathematics
[2] Institute of Information Technology,Faculty of Textile Technology
[3] University of Zagreb,Mathematics Department, Faculty of Food Technology and Biotechnology
[4] University of Zagreb,undefined
来源：
Mediterranean Journal of Mathematics | 2016年 / 13卷
关键词：
Primary 26D07; 26D15; 26D20; 26D99; Convex function; divided difference; Fink’s identity; Čebyšev functional; Grüss inequality; Ostrowski inequality; exponential convexity;
D O I：
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中图分类号：
学科分类号：
摘要：
We obtained useful identities via Fink’s identity, by which the inequality of Popoviciu for convex functions is generalized for higher order convex functions. We investigate the bounds for the identities related to the generalization of the Popoviciu inequality using inequalities for the Čebyšev functional. Some results relating to the Grüss- and Ostrowski-type inequalities are constructed. Further, we also construct new families of exponentially convex functions and Cauchy-type means by looking at linear functional associated with the obtained inequalities.
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页码：1495 / 1511
页数：16
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