Some characterizations of specially multiplicative functions

Some Characterizations of Specially Multiplicative Functions

A multiplicative function f is said to be specially multiplicative if there is a completelymultiplicative function fA such that f(m)f(n)= ∑ d|(m,n) f (mn/d)fA(d) for allm andn. For example, the divisor functions and Ramanujan’s τ-function are specially multiplicative functions. Some characterizations of specially multiplicative functions are given in the literature. In this paper, we provide so...

Variational Inequalities and Pseudomonotone Functions: Some Characterizations

The paper provides some characterizations of (strictly) pseudomonotone and (strictly) monotone functions by properties of the solutions to the associated variational inequality problems. Moreover, an economic interpretation of the results is offered.

Some Remarks about Additive and Multiplicative Functions

The present paper contains some results about the classical multiplicative functions (n), a(n) and also about general additive and multiplicative functions. (1) It is well known that n/{n) ^x.) It is known that both fi(x) and fï(x) are strictly inc...

Some Asymptotic Formulas for Multiplicative Functions

Variational characterizations of the effective multiplicative factor

We prove some inf–sup and sup–inf formulae for the so–called effective multiplication factor arising in the study of reactor analysis. We treat in a same formalism the transport equation and the energy–dependent diffusion equation.