The authors introduce the concept of thes-geometrically convex functions. By the well-known Hölder inequality, they establish some integral inequalities of Hermite-Hadamard type related to thes-geometrically convex functions and apply these inequalities to special means.
ABSTRACT:We introduce the notion of m-harmonic-arithmetically convex functions and establish some integral inequalities of Hermite-Hadamard type for these functions.
In the paper, the authors establish some new Hermite-Hadamard type inequalities for functions whose first derivatives are of convexity and apply these inequalities to construct inequalities of special means.
In [1, Definition 1.9], the concept "s-geometrically convex function" was introduced. Making use of [1, Lemma 2.1], Hölder's integral inequality, and other analytic techniques, some inequalities of Hermite-Hadamard type were established. However, there are some vital errors appeared in main results of the paper [1].
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