Reconsidering a functional equation arising from number theory
نویسنده
چکیده
In a recent paper Chávez and Sahoo considered the functional equation f(ux− vy, uy + v(x+ y)) = f(x, y)f(u, v), which arose in a number theoretical context. Unfortunately one of their results is incorrect. Here we reconsider the equation on various domains. We observe that it is in fact a multiplicative Cauchy equation in disguise. We also point out some remaining open problems.
منابع مشابه
Surface Tension Prediction of n-Alkanes by a Modified Peng-Robinson Equation of State Using the Density Functional Theory
Through this study, the ability of a modified Peng-Robinson (MPR) equation of state in predicting the surface tension of n-alkanes based on the density functional theory approach was investigated and compared with other studies. The interfacial layer thickness and the density profile were calculated simultaneously at different temperatures from triple point to near critical point using the modi...
متن کاملFrequency Analysis of Embedded Orthotropic Circular and Elliptical Micro/Nano-Plates Using Nonlocal Variational Principle
In this paper, a continuum model based on the nonlocal elasticity theory is developed for vibration analysis of embedded orthotropic circular and elliptical micro/nano-plates. The nano-plate is bounded by a Pasternak foundation. Governing vibration equation of the nonlocal nano-plate is derived using Nonlocal Classical Plate Theory (NCPT). The weighted residual statement and the Galerkin method...
متن کاملOn the Stability of a Sum Form Functional Equation of Multiplicative Type
The stability of a so-called sum form functional equation arising in information theory is proved under certain conditions.
متن کاملOn a Functional Equation Arising from a Queueing Model
Functional equations play an important role in many applications. They offer a powerful tool for narrowing the models used to describe many phenomena. In particular, a certain challenging class of functional equations arises recently from many applications like e.g. networks and databases. Usually, such class of equations stems when obtaining the generating functions of queueing systems distrib...
متن کاملOn Approximate Stationary Radial Solutions for a Class of Boundary Value Problems Arising in Epitaxial Growth Theory
In this paper, we consider a non-self-adjoint, singular, nonlinear fourth order boundary value problem which arises in the theory of epitaxial growth. It is possible to reduce the fourth order equation to a singular boundary value problem of second order given by w''-1/r w'=w^2/(2r^2 )+1/2 λ r^2. The problem depends on the parameter λ and admits multiple solutions. Therefore, it is difficult to...
متن کامل