Continuous solutions of Dirichlet problem to Hessian type equations for $(\omega,m)-\beta$-subharmonic functions on a ball in $\mathbb{C}^n$

In this paper, we investigate the continuity of solutions to the Dirichlet problem for complex Hessian-type equations associated with $(\omega, m)-\beta$-subharmonic functions on a ball in $\mathbb{C}^n$, where $\beta=d d^c\|z\|^2=\frac{i}{2} \sum_{j=1}^n d z_j \wedge d \bar{z}_j$ is denoted the flat metric on $\mathbb{C}^n$.