IJPAM: Volume 113, No. 3 (2017)

Title

APPROXIMATION OF ENTIRE FUNCTIONS
OF SLOW GROWTH

Authors

Ning Juhong$^1$, Chen Qing$^2$
$^{1,2}$College of Mathematics and Information Science
Jiangxi Normal University
Nanchang, Jiangxi, P.R. CHINA

Abstract

In this paper, first of all, we defined the generalized order and generalized type of Taylor entire function; Secondly, we show some interesting relationship on the maximum modulus, the maximum term and the coefficients of Taylor entire function; Finally, we study the polynomial approximation of entire functions in Banach spaces ($(B(p,q,k);f)$, Hardy spaces, Bergman spaces), the coefficient characterization of generalized type of Taylor entire function of slow growth has been obtained in terms of the approximation errors.

History

Received: September 25, 2016
Revised: December 25, 2016
Published: March 28, 2017

AMS Classification, Key Words

AMS Subject Classification: 30B50
Key Words and Phrases: Taylor entire function, generalized order, generalized type, approximation error.

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.

Bibliography

1
S.M. Shah, Polynomial approximation of an entire function and generalized orders, Journal of approximation theory, 4 (1977) 315-324,doi: https://doi.org/10.1016/0021-9045(77)90095-8.

2
S.K. Bajpai, G.P. Kapoor, and O.P. Juneja, On entire function of fast growth, Transactions of the american mathematical society, 203 (1975) 275-297, doi: https://doi.org/10.1090/S0002-9947-1975-0372200-0.

3
G.P. Kapoor, A. Nautiyal, Polynomial approximation of an entire function of slow growth, Journal of approximation theory, 32 (1981) 64-75, doi: https://doi.org/10.1016/0021-9045(81)90022-8.

4
A. Nautiyal, G.P. Kapoor, On the generalized orders of an entire function of slow growth, Indian journal of pure and applied mathematics, 11 (1982) 1246-1252.

5
R. Ganti, G.S. Srivastava, Approxiamtion of entire function of slow growth, General mathematics, 14 (2006) 59-76.

6
S.B. Vakarchuk, S.I. Zhir, On some problem of polynomial approximation of entire transcendental function, Ukrainian mathematical journal, 9 (2002) 1393-1401, doi: https://doi.org/10.1023/A:1023407416027.

7
M.I. Gvaradze, On the class of spaces of analytic functions. Matematicheskie zametki, 2 (1977), 141-150. doi: https://doi.org/10.1007/BF02320544.

6
S.B. Vakarchuk, On the best polynomial approximation in some Banach spaces for functions analytical in the unit disc, Mathematical notes, 4 (1994) 338-343, doi: https://doi.org/10.1007/BF02112471.

8
Y.Y. Kong , H.L. Gan, On orders and types of Dirichlet series of slow growth, Turkish journal of mathematics, 1 (2010) 1-11, doi: https://doi.org/10.3906/mat-0810-17.

How to Cite?

DOI: 10.12732/ijpam.v113i3.3 How to cite this paper?

Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 113
Issue: 3
Pages: 399 - 413


Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).