Inequalities for convex sequences and nondecreasing convex functions

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• 作者：Marek Niezgoda
• 关键词：Convex function ; Convex sequence ; Majorization ; Column stochastic matrix
• 刊名：Aequationes mathematicae
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：91
• 期：1
• 页码：1-20
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Analysis; Combinatorics;
• 出版者：Springer International Publishing
• ISSN：1420-8903
• 卷排序：91

文摘

In this paper, by using Wu–Debnath’s method, we establish inequalities of Hammer–Bullen type for convex sequences and nondecreasing convex functions. In particular, we give an extension of a recent Farissi’s inequality. By assuming the symmetry of an involved sequence, we derive an inequality of Fejér–Hammer–Bullen type for convex sequences. In addition, we establish some companions of an Hermite–Hadamard like inequality by Latreuch and Belaïdi. In our approach we use matrix methods based on column stochastic matrices.