  We initiate the study of Lie-Trotter means in JB-algebras, which is an
extension of Lie-Trotter formulas in JB-algebras. We show that two-variable
Lie-Trotter means include the weighted arithmetic mean, weighted harmonic mean,
weighted geometric mean, and weighted spectral geometric mean. Consequently,
several generalized Lie-Trotter formulas in JB-algebras are derived.
Additionally, we demonstrate that the Sagae-Tanabe mean and Hansen's induction
mean in JB-algebras are multivariable Lie-Trotter means. In the end, using
arithmetic-geometric-harmonic mean inequalities we provide a characterization
of multivariate Lie-Trotter means.
