ON TRIGONOMETRICALLY QUASI-CONVEX FUNCTIONS

In this paper, we introduce and study the concept of trigono-metrically quasi-convex function. We prove Hermite-Hadamard type in- equalities for the newly introduced class of functions and obtain some new Hermite-Hadamard inequalities for functions whose first derivative in absolute value, raised to a certain power which is greater than one, respectively at least one, is trigonometrically quasi-convex convex. We also extend our initial results to functions of several variables. Next, we point out some applications of our results to give estimates for the approximation error of the integral the function in the trapezoidal formula.