Exponential trigonometric convex functions and Hermite-Hadamard type inequalities

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-Işcan and improved power-mean integral inequalities give better approximations than that obtained with Hölder and improved power-mean integral inequalities.