On the mean values of an analytic function.

G. S. Srivastava; Sunita Rani

Annales Polonici Mathematici (1992)

  • Volume: 57, Issue: 2, page 149-155
  • ISSN: 0066-2216

Abstract

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Let f(z), z = r e i θ , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values I δ ( r ) and the iterated mean values N δ , k ( r ) of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).

How to cite

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G. S. Srivastava, and Sunita Rani. "On the mean values of an analytic function.." Annales Polonici Mathematici 57.2 (1992): 149-155. <http://eudml.org/doc/262448>.

@article{G1992,
abstract = {Let f(z), $z = re^\{iθ\}$, be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values $I_δ(r)$ and the iterated mean values $N_\{δ,k\}(r)$ of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).},
author = {G. S. Srivastava, Sunita Rani},
journal = {Annales Polonici Mathematici},
keywords = {analytic function; maximum term; order; type; mean values; order typ; convexity},
language = {eng},
number = {2},
pages = {149-155},
title = {On the mean values of an analytic function.},
url = {http://eudml.org/doc/262448},
volume = {57},
year = {1992},
}

TY - JOUR
AU - G. S. Srivastava
AU - Sunita Rani
TI - On the mean values of an analytic function.
JO - Annales Polonici Mathematici
PY - 1992
VL - 57
IS - 2
SP - 149
EP - 155
AB - Let f(z), $z = re^{iθ}$, be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values $I_δ(r)$ and the iterated mean values $N_{δ,k}(r)$ of f(z). A convexity result for the above mean values is obtained and their relative growth is studied using the order and type of f(z).
LA - eng
KW - analytic function; maximum term; order; type; mean values; order typ; convexity
UR - http://eudml.org/doc/262448
ER -

References

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  1. [1] R. P. Boas, Entire Functions, Academic Press, New York 1954. Zbl0058.30201
  2. [2] G. H. Hardy, The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14 (2) (1915), 269-277. Zbl45.1331.03
  3. [3] G. P. Kapoor, A note on the proximate order of functions analytic in the unit disc, Rev. Fac. Sci. Univ. d'Istanbul Sér. A 36 (1971), 35-40. Zbl0299.30021
  4. [4] L. R. Sons, Regularity of growth and gaps, J. Math. Anal. Appl. 24 (1968), 296-306. Zbl0195.08501

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