Generalization of Bohr-type Inequality in Analytic Functions

We mainly use the nonnegative continuous function {ζn(r)}n≥0 to redefine the Bohr radius for the class of analytic functions satisfying Ref(z) < 1 in the unit disk |z| < 1 and redefine the Bohr radius of the alternating series Af(r) with analytic functions f of the form ( Formula presented). 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 Mf(r) and the odd and the even bits of f(z) are also established. We will prove that most of results are sharp.