Abstract We consider a class of generalized convex functions, which are defined according to a pair of quasi-arithmetic means and called ( M ϕ , M ψ ) -convex functions, and establish various Fejer type inequalities for such a function class. These inequalities not merely provide a natural and intrinsic characterization of the ( M ϕ , M ψ ) -convex functions, but actually offer a generalization and refinement of the most part of the concrete Hermite-Hadamard and Fejer type inequalities obtained in earlier studies for different kinds of convexity and fractional integrals. Applications to inequalities involving the gamma function and special means are also included.

中文翻译：

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根据一对拟算术均值和不等式的凸性

摘要 我们考虑一类根据一对拟算术均值定义的广义凸函数，称为( M ϕ , M ψ ) -凸函数，并为此类函数建立各种Fejer型不等式。这些不等式不仅提供了 ( M ϕ , M ψ ) -凸函数的自然和内在特征，而且实际上提供了对早期研究中针对不同类型的具体 Hermite-Hadamard 和 Fejer 类型不等式的大部分进行概括和改进。各种凸积分和分数积分。还包括对涉及伽马函数和特殊方法的不等式的应用。