On Fejér-type inequalities for generalized trigonometrically and hyperbolic k-convex functions - Dragomir, Silvestru Sever; Jleli, Mohamed; Samet, Bessem (Demonstratio mathematica, 2024)
For , , and , where is an open interval of , we consider the set of functions satisfying the second-order differential inequality in . The considered set includes several classes of generalized convex functions from the literature. In particular, if and , , we obtain the class of trigonometrically -convex functions, while if and , , we obtain the class of hyperbolic -convex functions. In this article, we establish a Fejér-type inequality for the introduced set of functions without any symmetry condition imposed on the weight function and discuss some special cases of weight functions. Moreover, we provide characterizations of the classes of trigonometrically and hyperbolic -convex functions.