On convergence of formal Dulac series, satisfying an algebraic $q$-difference equation

An algebraic $q$-difference equation for $\mathrm{\mid }q\mathrm{\mid }>1$ is considered. A sufficient condition is proposed for the convergence of a solution to such an equation in the form of a Dulac series within a sector centered at the origin. An example illustrating the application of this sufficient condition is provided.