Bohr’s inequalities associated with the set of all sequences of nonnegative continuous functions - Biswas, Raju; Mandal, Rajib (Ukrains’kyi Matematychnyi Zhurnal, 2025)
UDC 517.5 We establish several sharp versions of Bohr’s inequalities for the class of K-quasiconformal sense-preserving harmonic mappings on the unit disk D := {z C|z| < 1} by using a sequence {Ψ_n(r)}_n=0^∞ of nonnegative continuous functions defined on [0,1) and such that the series _n=0^∞ Ψ_n(r) converges locally uniformly in [0,1). As an application, we deduce several well-known results, as well as numerous improved and refined Bohr’s inequalities for harmonic mappings in the unit disk D.