Alienation of Drygas’ and Cauchy’s Functional Equations

Abstract

Inspired by the papers [2, 10] we will study, on 2-divisible groups that need not be abelian, the alienation problem between Drygas’ and the exponential Cauchy functional equations, which is expressed by the equation f(x+y)+g(x+y)g(x-y)=f(x)f(y)+2g(x)+g(y)+g(-y).f\left( {x + y} \right) + g\left( {x + y} \right)g\left( {x - y} \right) = f\left( x \right)f\left( y \right) + 2g\left( x \right) + g\left( y \right) + g\left( { - y} \right).

Keywords

• alienation
• exponential cauchy equation
• additive cauchy equation
• logarithmic cauchy equation
• drygas’ functional equation
• 39b32
• 39b42
• 39b72