Let f(z), , be analytic in the finite disc |z| < R. The growth properties of f(z) are studied using the mean values and the iterated mean values 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).
@article{bwmeta1.element.bwnjournal-article-apmv57z2p149bwm,
author = {G. S. Srivastava and Sunita Rani},
title = {On the mean values of an analytic function.},
journal = {Annales Polonici Mathematici},
volume = {57},
year = {1992},
pages = {149-155},
zbl = {0759.30002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p149bwm}
}
G. S. Srivastava; Sunita Rani. On the mean values of an analytic function.. Annales Polonici Mathematici, Tome 57 (1992) pp. 149-155. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv57z2p149bwm/
[000] [1] R. P. Boas, Entire Functions, Academic Press, New York 1954. | Zbl 0058.30201
[001] [2] G. H. Hardy, The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14 (2) (1915), 269-277. | Zbl 45.1331.03
[002] [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. | Zbl 0299.30021
[003] [4] L. R. Sons, Regularity of growth and gaps, J. Math. Anal. Appl. 24 (1968), 296-306. | Zbl 0195.08501