The deformed Hermitian-Yang-Mills equation on almost Hermitian manifolds

In this paper, we consider the deformed Hermitian-Yang-Mills equation on closed almost Hermitian manifolds. In the case of the hypercritical phase, we derive a priori estimates under the existence of an admissible $${\cal C}$$ -subsolution. As an application, we prove the existence of solutions for the deformed Hermitian-Yang-Mills equation under the condition of existence of a supersolution.