In this paper we introduce and study the concept of trigonometrically convex function, which is a special case of h-convex functions. The class of trigonometrically convex func-tion is large enough to include the class of non-negative convex functions. We prove two Hermite-Hadamard type inequalities for the newly introduced class of functions. We also obtain two 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 trigonometrically convex.
