Generalization of Bohr-type inequality in analytic functions

Abstract

This paper mainly uses the nonnegative continuous function {ζ n (r)} ∞ n=0 to redefine the Bohr radius for the class of analytic functions satisfying Re f (z) < 1 in the unit disk |z| < 1 and redefine the Bohr radius of the alternating series A f (r) with analytic functions f of the form f (z) = ∞ n=0 a pn+m z pn+m in |z| < 1. In the latter case, one can also get information about Bohr radius for even and odd analytic functions. Moreover, the relationships between the majorant series M f (r) and the odd and even bits of f (z) are also established. We will prove that most of results are sharp.

A generalized Bohr-Rogosinski phenomenon

“…In context of the above problem and Muhanna [19], we now describe the notion of generalized Bohr-Rogosinski phenomenon here below, in terms of subordination, following the recent development as seen in [28,29,30]. Then we say S(f ) satisfies the Generalized Bohr-Rogosinski phenomenon, if there exists a constant r 0 ∈ (0, 1] such that…”