Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$

Abstract

In this paper, the concept of the $(p,h)$-convex function is introduced, which generalizes the $p$-convex function and the $h$-convex function, and Hermite-Hadamard type inequalities for $(p,h)$-convex functions on $\mathbb{R}^n$ are established. Furthermore, some mappings related to the above inequalities are studied and some known results are generalized.

Keywords

• the $p$-convex set
• the $(p,h)$-convex function,
• Hermite-Hadamard type inequalities
• mapping

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