The log-concavity of the Hölder mean of two numbers, as a function of its index, is presented first. The notion of -cevian of a triangle is introduced next, for any real number . We use this property of the Hölder mean to find the smallest index such that the length of an -cevian of a triangle is less than or equal to the -Hölder mean of the lengths of the two sides of the triangle that are adjacent to that cevian.
"Log-concavity of Hölder means and an application to geometric inequalities." Involve 12 (4) 671 - 686, 2019. https://doi.org/10.2140/involve.2019.12.671