Harmonic analogue of Bohr phenomenon of certain classes of univalent and analytic functions - Ahamed, Molla Basir; Allu, Vasudevarao (MATHEMATICA SCANDINAVICA, 2023)
A class F consisting of analytic functions f(z)=_n=0^∞ a_nz^n in the unit disk D={zC:z vert <1} is said to satisfy Bohr phenomenon if there exists an r_f>0 such that _n=1^∞ a_n vert r^n≤ d(f(0),D) for every function fF , and z vert =r≤ r_f . The largest radius r_f is known as the Bohr radius and the inequality _n=1^∞ a_n vert r^n≤ d(f(0),f(D)) is known as the Bohr inequality for the class F , where d is the Euclidean distance. In this paper, we prove several sharp improved and refined versions of Bohr-type inequalities in terms of area measure of functions in a certain subclass of analytic and univalent (i.e. one-to-one) functions. As a consequence, we obtain several interesting corollaries on the Bohr-type inequality for the class which are the harmonic analogue of some Bohr-type inequality for the class of analytic functions.