(untitled) (European Journal of Pure and Applied Mathematics, 2025)
Möbius addition is a non-associative binary operation defined on the complex open unit disk D = {zC:|z|<1} by a_M b = a+b1+ab, and Möbius’s Exponential Equation is a non-linear functional equation of the form L(a_M b) = L(a)L(b), where L is a complex-valued function defined on D. In [Aequat. Math. 91 (2017), 491–503], the authors address the problem of determining the solutions to Möbius’s Exponential Equation. In this paper, we determine the complete list of solutions to Möbius’s Exponential Equation using an algebraic approach.