Inequalities characterizing linear-multiplicative functionals

We prove,in an elementary way,that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities,then it is a linear and multiplicative functional. moreover,we determine all jensen concave and supermultiplicative operators t: c x → c y,where x and y are compact hausdorff spaces. © 2015 włodzimierz fechner.