In this paper, we prove several sharp Bohr-type and Bohr-Rogosinski-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{ D}$, whose analytic part is subordinate to a function belonging to the class of concave univalent functions on $\mathbb{ D}$. In addition, we derive Bohr-type inequalities for $K$-quasiconformal, sense-preserving harmonic mappings on $\mathbb{ D}$, where the analytic part is subordinate to a function from the Ma-Minda class of convex and starlike functions. The results generalize several existing results.
Categories: math.CV