On the mean values of an analytic function.

• Autorzy: G. S. Srivastava , Sunita Rani
• Języki publikacji: EN

Abstrakty

EN

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).

Słowa kluczowe

EN

analytic function; maximum term; order; type; mean values

Kategorie tematyczne

• 30B10: Power series (including lacunary series)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1992
• Tom: 57
• Numer: 2
• Strony: 149-155

Daty

wydano

1992

otrzymano

1991-04-30

Twórcy

autor

G. S. Srivastava

• Department of Mathematics, University of Roorkee, Roorkee 247667, India

autor

Sunita Rani

• Department of Mathematics, University of Roorkee, Roorkee 247667, India

Bibliografia

• [1] R. P. Boas, Entire Functions, Academic Press, New York 1954.
• [2] G. H. Hardy, The mean value of the modulus of an analytic function, Proc. London Math. Soc. 14 (2) (1915), 269-277.
• [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.
• [4] L. R. Sons, Regularity of growth and gaps, J. Math. Anal. Appl. 24 (1968), 296-306.