Levinson’s type generalization of the Jensen inequality and its converse for real Stieltjes measure
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- 作者：Rozarija Mikić ; Josip Pečarić ; Mirna Rodić
- 关键词：Jensen’s inequality ; converse Jensen’s inequality ; Hermite ; Hadamard’s inequality ; Giaccardi’s inequality ; Levinson’s inequality ; Green function ; mean ; value theorems
- 刊名：Journal of Inequalities and Applications
- 出版年：2017
- 出版时间：December 2017
- 年：2017
- 卷：2017
- 期：1
- 全文大小：1648KB
- 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
- 出版者：Springer International Publishing
- ISSN：1029-242X
- 卷排序：2017
文摘
We derive the Levinson type generalization of the Jensen and the converse Jensen inequality for real Stieltjes measure, not necessarily positive. As a consequence, also the Levinson type generalization of the Hermite-Hadamard inequality is obtained. Similarly, we derive the Levinson type generalization of Giaccardi’s inequality. The obtained results are then applied for establishing new mean-value theorems. The results from this paper represent a generalization of several recent results.