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Paper's Title:

The Bernoulli Inequality in Uniformly Complete f-algebras with Identity

Author(s):

Adel Toumi and Mohamed Ali Toumi

Laboratoire de Physique des Liquides Critiques, Département de Physique, Faculté des Sciences de Bizerte, 7021, Zarzouna, Bizerte, TUNISIA
Adel.Toumi@fst.rnu.tn

Département de Mathématiques, Faculté des Sciences de Bizerte, 7021, Zarzouna, Bizerte, TUNISIA
MohamedAli.Toumi@fsb.rnu.tn


Abstract:

The main purpose of this paper is to establish with a constructive proof the Bernoulli inequality: let A be a uniformly complete f-algebra with e as unit element, let 1<p<∞, then

(e+a)p≥e+pa

for all a∈A+. As an application we prove the Hölder inequality for positive linear functionals on a uniformly complete f-algebra with identity by using the Minkowski inequality.

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