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.