Jensen-Type Inequalities, Montgomery Identity and Higher-Order Convexity

被引:0
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作者
Marija Bošnjak
Mario Krnić
Josip Pečarić
机构
[1] University of Slavonski Brod,Department of Mathematics, Mechanical Engineering Faculty
[2] University of Zagreb,Faculty of Electrical Engineering and Computing
[3] Croatian Academy of Sciences and Arts,Department of Mathematical, Physical and Chemical Sciences
来源
Mediterranean Journal of Mathematics | 2022年 / 19卷
关键词
Jensen inequality; Montgomery identity; Lah–Ribarič inequality; superadditivity; power mean; 26D10; 26D15.;
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摘要
Motivated by some recent results known from the literature, in this paper, we establish a class of Jensen-type inequalities referring to functions of an even degree of convexity. The main idea of proving our results is a transformation of the classical Jensen functional via the Montgomery identity which is suitable to study in companion with the higher-order convexity. In such a way, we obtain superadditivity and monotonicity relations that correspond to the Jensen functional equipped with a function of an even degree of convexity. As an application, we obtain some new bounds for the differences of power means. Furthermore, we also establish some new Hölder-type inequalities. Finally, we study the Lah–Ribarič inequality in the above-described setting.
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