An extension of Peleg's inequality

Abstract

In this note we prove an extension of a remarkable result due toB. Peleg. Peleg’s result concerns with the simultaneous validity of a set ofinequalities for families of functions defined on a finite product of standardsimplices in finite dimensional spaces. The main result we prove here providesan extension of that result to the case of functions defined on a rather generalproduct of simplices. Some topological requirements lead us to deal with thisproblem from a functional point of view.