Affiliation:
1. Institut Préparatoire aux études d’ingenieurs de Tunis + Faculté des Sciences de Tunis, Campus Universitaire El-Manar, El Manar Tunis, Tunisia
Abstract
We prove among others results that the harmonic mean of ?q(x) and ?q(1/x)
is greater than or equal to 1 for arbitrary x > 0, and q ? J where J is a
subset of [0,+?). Also, we prove that there is a unique real number p0 ? (1,
9/2), such that for q ? (0, p0), ?q(1) is the minimum of the harmonic mean
of ?q(x) and q(1/x) for x > 0 and for q ? (p0,+?), ?q(1) is the maximum.
Our results generalize some known inequalities due to Alzer and Gautschi.
Publisher
National Library of Serbia