Log and harmonically log-convex functions related to matrix norms

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.

Refinements to Hadamard’s Inequality for Log-Convex Functions

Fractional Hermite-Hadamard type inequalities for n-times log-convex functions

In this paper, we establish some Hermite-Hadamard type inequalities for function whose n-th derivatives are logarithmically convex by using Riemann-Liouville integral operator.

Convex Hull with Optimal Query Time and O ( log n · log log n ) Update Time

The dynamic maintenance of the convex hull of a set of points in the plane is one of the most important problems in computational geometry. We present a data structure supporting point insertions in amortized O(log n · log log logn) time, point deletions in amortized O(log n · log logn) time, and various queries about the convex hull in optimal O(log n) worst-case time. The data structure requi...

The Sugeno fuzzy integral of log-convex functions

*Correspondence: [email protected] 1Department of Mathematics, Faculty of Mathematics, Statistics and Computer Sciences, Semnan University, Semnan, 35195-363, Iran Full list of author information is available at the end of the article Abstract In this paper, we give an upper bound for the Sugeno fuzzy integral of log-convex functions using the classical Hadamard integral inequality. We pr...