id author title date pages extension mime words sentence flesch summary cache txt ejpam-6041 Maungchang, Rasimate ; Atiponrat, Watchareepan ; Suwansri, Tarid ; Wattanapan, Jaturon ; Suksumran, Teerapong The Complete List of Solutions to M\"{o}bius's Exponential Equation 2025 8 .pdf application/pdf 3381 202 70 Möbius addition is a non-associative binary operation defined on the complex open unit disk D = {z ∈ C : |z| < 1} by a ⊕M b = a+ b 1 + 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. 2020 Mathematics Subject Classifications: 39B32, 30D05, 20N05 Key Words and Phrases: Möbius addition, Möbius’s Exponential Equation, associator function, gyrogroup, non-linear equation 1. cache/ejpam-6041.pdf txt/ejpam-6041.txt