In this manuscript, we introduce and study the concept of exponential trigonometric convex functions and their some algebraic properties. We obtain Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain some refinements of the Hermite-Hadamard inequality for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is exponential trigonometric convex function. It has been shown that the result obtained with Hölder-İşcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.

中文翻译：

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指数三角凸函数和Hermite-Hadamard型不等式

在本文中，我们介绍并研究了指数三角凸函数的概念及其一些代数性质。对于新引入的函数类，我们获得了Hermite-Hadamard型不等式。我们还对函数的Hermite-Hadamard不等式进行了一些改进，这些函数的绝对值的一阶导数分别提高到大于1或至少1的一定幂次，是指数三角凸函数。结果表明，用Hölder-İşcan和改进的幂均值积分不等式获得的结果比用Hölder和改进的幂均值积分不等式得到的结果更好。