Korean J. Math.  Vol 29, No 1 (2021)  pp.105-120
DOI: https://doi.org/10.11568/kjm.2021.29.1.105

Relative logarithmic order of an entire function

Chinmay Ghosh, Anirban Bandyopadhyay, Soumen Mondal

Abstract


In this paper, we extend some results related to the growth rates of entire functions by introducing the relative logarithmic order $\rho _{g}^{l}(f)$ of a nonconstant entire function $f$ with respect to another nonconstant entire function $g.$ Next we investigate some theorems related the behavior of $\rho _{g}^{l}(f)$. We also define the relative logarithmic$\ $proximate order of $f$ with respect to $g$ and give some theorems on it.


Keywords


property (A), relative order, logarithmic order, relative logarithmic order, relative logarithmic proximate order

Subject classification

30D20; 30D30

Sponsor(s)



Full Text:

PDF

References


L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209– 229. (Google Scholar)

P. T. Y. Chern, On meromorphic functions with finite logarithmic order, Amer. Math. Soc. 358 (2) (2005), 473–489. (Google Scholar)

I. Chyzhykov, J. Heittokangas and J. R ̈atty ̈a:, Finiteness of φ-order of solutions of linear differential equations in the unit disc., J. Anal. Math. 109 (2009), 163–198. (Google Scholar)

O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p, q)−order and lower (p, q)−order of an entire function, Journal fu ̈r die Reine und Angewandte Mathematik 282 (1976), 53–67. (Google Scholar)

D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411–414. (Google Scholar)

S. M. Shah, On proximate orders of integral functions, Bull. Amer. Math. Soc. 52 (1946), 326– 328. (Google Scholar)

G. Valiron, Lectures on the general theory of integral functions, Toulouse, 1923. (Google Scholar)


Refbacks

  • There are currently no refbacks.


ISSN: 1976-8605 (Print), 2288-1433 (Online)

Copyright(c) 2013 By The Kangwon-Kyungki Mathematical Society, Department of Mathematics, Kangwon National University Chuncheon 21341, Korea Fax: +82-33-259-5662 E-mail: kkms@kangwon.ac.kr