Refinements to Hadamard’s Inequality for Log-Convex Functions

Refinements to Hadamard’s Inequality for Log-Convex Functions

JENSEN’S INEQUALITY FOR GG-CONVEX FUNCTIONS

In this paper, we obtain Jensen’s inequality for GG-convex functions. Also, we get in- equalities alike to Hermite-Hadamard inequality for GG-convex functions. Some examples are given.

An inequality related to $eta$-convex functions (II)

Using the notion of eta-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite-Hadamard-Fejer inequality for differentiable mappings. Also as an application we give an error estimate for midpoint formula.

Inequalities for 3-log-convex Functions

This note gives a simple method for obtaining inequalities for ratios involving 3log-convex functions. As an example, an inequality for Wallis’s ratio of Gautchi-Kershaw type is obtained. Inequalities for generalized means are also considered.

Convex SO(N)× SO(n)-invariant Functions and Refinements of Von Neumann’s Inequality

A function f : Mn(R)→ [−∞,∞] is said to be SO(n)× SO(n)-invariant if ∀ξ ∈Mn(R), ∀Q,R ∈ SO(n), f(QξR) = f(ξ). The specification of an SO(n)× SO(n)-invariant function f is easily seen to be equivalent to that of a function g : R → R which is invariant under ∗EPFL, CH-1015 Lausanne, Switzerland. Email: [email protected]. †Université Paul Sabatier, F-31062 Toulouse cedex 4, France. Email: m...