ABSTRACT. Let (*) A*) = V"z " n=0 be a transcendental entire function. Set Ai(r) = max \fiz)\, m(r) = max {la \r "} \z\=r n>0and N(r) = max {XJm(r) = \a"\r "}. For the case q = 2, these notions are due to Whittakar and Shah respectively.

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1. Let be an analytic function with radius of convergence R (0 < R < ∞). Setand let the order p and lower order ⋋ of f(z) be defined bywhere x = Rr/(R — r). If 0 < ᑭ < ∞, we define the type T and lower type t of f(z) byAlso, if 0 < ᑭ < ∞, define the “growth numbers” 𝛄 and δ byThe purpose of our discussion will be to obtain some inequalities involving the growth constants defined above.

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