In this paper, we investigate the Dirichlet problem concerning the homogeneous mixed Hessian type equation in the convex cone \({\widetilde \Gamma}_{k}\) with prescribed asymptotic behavior at 0 ∈ Ω, where Ω is a strictly (k − 1)-convex bounded domain. By constructing approximating solutions, we establish the corresponding theorems on the existence and uniqueness of C1,1 solutions. The key is to construct subsolutions for the approximating non-degenerate mixed Hessian type equation. Moreover, our main technique is to establish uniform gradient estimates and second-order estimates which are independent of the approximation.
