Relative $( p,q,t) L$-th Type and Relative $( p,q,t) L$-th Weak Type Oriented Growth Properties of Composite Entire Functions

Year 2021, Volume: 9 Issue: 1, 65 - 75, 28.04.2021

Tanmay Biswas , Chınmay Bıswas

https://izlik.org/JA83JG23WT

Abstract

In the paper some new results depending on the comparative growth properties of composite entire functions using relative $( p,q,t) L$-th order, relative $( p,q,t) L$-th type\ and relative $( p,q,t) L$-th weak type of entire function with respect to another entire function are established.

Keywords

Entire function , relative (p,q,t)L-th order , relative (p,q,t)L-th type , relative (p,q,t)L-th weak type , growth , slowly changing function

References

• [1] Bernal, L., Orden relative de crecimiento de funciones enteras , Collect. Math., Vol: 39 (1988), 209-229.
• [2] Biswas, T., Relative (p,q,t)-th order and relative (p,q,t)-th type based some growth aspects of composite entire and meromorphic functions, Honam Math. J., Vol: 4, No. 3 (2019), 463-487
• [3] Biswas, T., Some results relating to sum and product theorems of relative (p,q,t)L-th order and relative (p,q,t)L-th type of entire functions, Korean J. Math., Vol: 26, No. 2 (2018), 215-269.
• [4] Clunie, J., The composition of entire and meromorphic functions, Mathematical Essays dedicated to A. J. Macintyre, Ohio University Press (1970), 75-92.
• [5] Juneja, O. P., Kapoor, G. P. and Bajpai, S. K., On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math., Vol: 282 (1976), 53-67.
• [6] Somasundaram, D. and Thamizharasi, R., A note on the entire functions of L-bounded index and L type, Indian J. Pure Appl. Math., Vol: 19, No. 3 (1988), 284-293.
• [7] Shen, X., Tu, J. and Xu, H. Y.,Complex oscillation of a second-order linear differential equation with entire coefficients of [p,q]-j order, Adv. Difference Equ. Vol: 2014(1): 200, (2014), 14 pages, http://www.advancesindifferenceequations.com/content/2014/1/200.
• [8] Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol: 69 (1963), 411-414.
• [9] Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, Company, New York, 1949.