Approximately two-dimensional harmonic \((p_{1},h_{1})\) - \((p_{2},h_{2})\) -convex functions and related integral inequalities

[摘要] The aim of this study is to introduce the notion of two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We show that the new class covers many new and known extensions of harmonic convex functions. We formulate several new refinements of Hermite–Hadamard like inequalities involving two-dimensional approximately harmonic $(p_{1},h_{1})$ - $(p_{2},h_{2})$ -convex functions. We discuss in detail the special cases that can be deduced from the main results of the paper.

[学科分类] 电力

[关键词] Hermite–Hadamard inequality;Hölder inequality;Convexity