Improving Jensen-type Inequalities Via the Sum of the Lidstone Polynomials

被引：0
作者：
Mario Krnić
机构：
[1] Faculty of Electrical Engineering and Computing,University of Zagreb
来源：
Bulletin of the Malaysian Mathematical Sciences Society | 2024年 / 47卷
关键词：
Jensen Inequality; Lidstone Polynomial; Green Function; Absolute Convexity; Complete Convexity; 26D15; 26A51;
D O I：
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学科分类号：
摘要：
We aim to establish refinements of the Jensen inequality for the classes of completely convex and absolutely convex functions. In the first case the refinement is expressed in terms of the alternating sum of Lidstone polynomials, while in the second case we deal with the sum of the Lidstone polynomials. As an application, more accurate power mean inequalities are derived. In particular, we obtain strengthened versions of arithmetic–geometric mean inequality in a difference and a quotient form. Finally, we also establish more accurate form of the Hölder inequality.
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