Generalized convex functions and second order differential inequalities

Generalized Convex Functions and Second Order Differential Inequalities

Generalized geometrically convex functions and inequalities

In this paper, we introduce and study a new class of generalized functions, called generalized geometrically convex functions. We establish several basic inequalities related to generalized geometrically convex functions. We also derive several new inequalities of the Hermite-Hadamard type for generalized geometrically convex functions. Several special cases are discussed, which can be deduced ...

Inequalities for discrete higher order convex functions

[1] E. BOROS AND A. PRÉKOPA, Closed Form Two-Sided Bounds for Probabilities That Exactly r and at Least r out of n Events Occur, Mathematics of Operations Research, 14 (1989), 317–342. [2] D. DAWSON AND A. SANKOFF, An Inequality for Probabilities, Proceedings of the American Mathematical Society, 18 (1967), 504–507. [3] H.P. EDMUNDSON, Bounds on the Expectation of a Convex Function of a Random ...

(m1,m2)-AG-Convex Functions and Some New Inequalities

In this manuscript, we introduce concepts of (m1,m2)-logarithmically convex (AG-convex) functions and establish some Hermite-Hadamard type inequalities of these classes of functions.

Hermite-Hadamard inequalities for $mathbb{B}$-convex and $mathbb{B}^{-1}$-convex functions

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.