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On the auxiliary geometric mean of entire functions. (English) Zbl 0592.30031

Summary: We have introduced a new geometric mean \(J_{k,m}(r)\) which we shall term as auxiliary geometric mean (a.g.m.) of an entire function \(f(z)=\sum^{\infty}_{n=0}a_ nz^ n\), \(z=r \exp (i\theta)\) and have obtained a few growth relations of this mean with respect to other known functions such as G(r) and n(r) etc. Some theorems are the generalizations and combinations of many results obtained by different authors.

MSC:

30D15 Special classes of entire functions of one complex variable and growth estimates
30D20 Entire functions of one complex variable (general theory)
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