Regularization and Hölder continuity for complex Hessian equations on Hermitian manifolds

Let $(M,ω)$ be a compact Hermitian manifold, and let $Γ$ be a symmetric convex cone. We develop a quantitative regularization method for $Γ$-admissible functions. As an application, we prove Hölder continuity for every pluripotential solution of complex $m$-Hessian equations whose right-hand sides b