Abstract In this paper, we establish Jensen’s inequality for s -convex functions in the first sense. By using inequalities, obtain some Cauchy type means p and Also, by Hermite–Hadamard inequalities respective generalized convex functions, find new means.

In this paper we find a characterization type result for (η1,η2)-convex functions. The Fejér integral inequality related to (η1,η2)-convex functions is obtained as a generalization of Fejér inequality related to the preinvex and η-convex functions. Also some Fejér trapezoid and midpoint type inequalities are given in the case that the absolute value of the derivative of considered function is (...

Making use of the generalized hypergeometric functions, we introduce some generalized class of k−uniformly convex and starlike functions and for this class, we settle the Silverman’s conjecture for the integral means inequality. In particular, we obtain integral means inequalities for various classes of uniformly convex and uniformly starlike functions in the unit disc.

The generalized mean function has been widely used in convex analysis and mathematical programming. This paper studies a further generalization of such a function. A necessary and sufficient condition is obtained for the convexity of a generalized function. Additional sufficient conditions that can be easily checked are derived for the purpose of identifying some classes of functions which guar...

In this paper, we introduce some new subclasses of analytic functions related to starlike, convex, close-to-convex and quasi-convex functions defined by using a generalized operator and the differential subordination principle. Inclusion relationships for these subclasses are established. Moreover, we introduce some integral-preserving properties. Key-Words: Starlike function; Convex function; ...

Hermite-Hadamard inequality is one of the fundamental applications of convex functions in Theory of Inequality. In this paper, Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions are proven.