In this paper, our interest is devoted to study the convex combinations of the form (1 − λ) f + λ, where λ ∈ (0, 1), of biholomorphic mappings on the Euclidean unit ball B n in the case of several complex variables. Starting from a result proved by S. Trimble [26] and then extended by P.N. Chichra and R. Singh [3, Theorem 2] which says that if f is starlike such that Re[ f ′ (z)] > 0, then (1 − λ)z + λ f (z) is also starlike, we are interested to extend this result to higher dimensions. In the first part of the paper, we construct starlike convex combinations using the identity mapping on B n and some particular starlike mappings on B n. In the second part of the paper, we define the class L * λ (B n) and prove results involving convex combinations of normalized locally biholomorphic mappings and Loewner chains. Finally, we propose a conjecture that generalize the result proved by Chichra and Singh.