Inspired by work of R. M. Aron and R. H. Lohman, Gert K. Pedersen introduced a geometric function, which is defined on the unit ball of a C*-algebra and called the λ_u-function. Our goal here is to extend the notion of a λ_u-function to the context of JB*-algebras. We study convex combinations of elements in a JB*-algebra using the λ_u-function and earlier results we have obtained on the geometry of JB*-algebras. A formula to compute λ_u-function is obtained for invertible elements in a JB*-algebra. In the course of our analysis, some C*-algebra results due to G. K. Pedersen, C. L. Olsen and M. R\o rdam are extended to general JB*-algebras.