Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-19T18:31:39.363Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

1. Fricke, G. H., Shah, S. M., and Sisarcick, W. C., A characterization of entire functions of exponential type and M-bounded index (to appear).Google Scholar
2. Lakshminarasimhan, T. V., Inequalities between means involving an entire function or its real part and means involving the derived function, J. Math. Anal. Appl. 27 (1969), 624–635.Google Scholar
3. Shah, S. M., The maximum term of an entire series 111, Quart. J. Math. Oxford Ser. 19 (1948), 220–223.Google Scholar
4. Singh, S. K., On the maximum term and the rank of an entire function, Acta Math. 94 (1955), 1–11.Google Scholar
5. Sons, L. R., Regularity of growth and gaps, J. Math. Anal. Appl. 24 (1968), 296–306.Google Scholar