Trigonometrically Convex Functions

Abstract

in this thesis we study some properties of trigonometrically -convex functions which analogous to those of classical convex functions. Moreover, we introduce a de nition of conjugate trigonometrically -convex functions by using Young's inequality which plays an important role in linking the concept of duality between trigonometrically -convex functions. Furthermore, we show that the integration of any increasing function is trigonometrically -convex. In addition, we established some new integral inequalities of P olya, Ste ensen, Young, Hermite-Hadamard and Cauchy-Schwarz types for trigonometrically -convex functions. Also, we study some properties of the multiplication of two trigonometrically -convex functions, and prove the non negative convex function is trigonometrically -convex functions. Finally, we give applications of trigonometrically convex functions in di erent elds.