On an alternative Cauchy equation.
The aim of this note is to characterize the real coefficients p₁,...,pₙ and q₁,...,qₖ so that be valid whenever the vectors x₁,...,xₙ, y₁,...,yₖ satisfy y₁,...,yₖ ⊆ convx₁,...,xₙ. Using this characterization, a class of generalized weighted quasi-arithmetic means is introduced and several open problems are formulated.
In this work we apply the method of a unique partition of a complex function of complex variables into symmetrical functions to solving a certain type of functional equations.