On some inequalities of H. Kober

Throughout this paper q1,q2,… are positive and x1,x2,… non-negative real numbers. When q1+…+ qn = 1, we define Δn, Sn and Σn as follows:andWe use the term ‘comparable’ in Kober's(2) sense. Two functions f(x1, …, xn) and g(x1, …, xn) are comparable if and only if αg ≤ f ≤ βg for some positive constants α and β.