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Analogues of Entire Function Inequalities for an Analytic Function

Published online by Cambridge University Press:  20 November 2018

S. K. Bajpai  and
Joseph Tanne
S. K. Bajpai
Affiliation:
Clark University, Worcester, Massachusetts
Joseph Tanne
Affiliation:
Clark University, Worcester, Massachusetts
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1. Let be an analytic function with radius of convergence R (0 < R < ∞). Set

and let the order p and lower order ⋋ of f(z) be defined by

where x = Rr/(R — r). If 0 < ᑭ < ∞, we define the type T and lower type t of f(z) by

Also, if 0 < ᑭ < ∞, define the “growth numbers” 𝛄 and δ by

The purpose of our discussion will be to obtain some inequalities involving the growth constants defined above.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 2 , 01 April 1975 , pp. 286 - 293
Copyright
Copyright © Canadian Mathematical Society 1975

References

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