Relative logarithmic order of an entire function
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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.
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References
[1] L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209– 229. Google Scholar
[2] P. T. Y. Chern, On meromorphic functions with finite logarithmic order, Amer. Math. Soc. 358 (2) (2005), 473–489. Google Scholar
[3] 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
[4] 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
[5] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411–414. Google Scholar
[6] S. M. Shah, On proximate orders of integral functions, Bull. Amer. Math. Soc. 52 (1946), 326– 328. Google Scholar
[7] G. Valiron, Lectures on the general theory of integral functions, Toulouse, 1923. Google Scholar