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 $\beta =d{d}^c\mathrm{\parallel }z{\mathrm{\parallel }}^2=\frac{i}{2}{\sum }_{j=1}^{n}d{z}_j\wedge d{\bar{z}}_j$ is denoted the flat metric on ${\mathbb{C}}^n$.