# On the mean values of an analytic function.

Annales Polonici Mathematici (1992)

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

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topG. 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

top- [1] R. P. Boas, Entire Functions, Academic Press, New York 1954. Zbl0058.30201
- [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] 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] L. R. Sons, Regularity of growth and gaps, J. Math. Anal. Appl. 24 (1968), 296-306. Zbl0195.08501

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