Growth estimates of entire functions with the help of their relative L^{∗}-types and relative L^{∗}- weak types

Year 2019, Volume: 68 Issue: 1, 136 - 148, 01.02.2019

Sanjib Kumar Datta , Tanmay Biswas

https://doi.org/10.31801/cfsuasmas.443685

Abstract

In this paper we attempt to prove some results related to the growth rates of entire functions on the basis of relative L^{∗}-type and relative L^{∗}-weak type of an entire function with respect to another entire function.

Keywords

Entire function, slowly changing function, relative L^{∗}-order (relative L^{∗}-lower order), relative L^{∗}-type (relative L^{∗}- lower type), relative L^{∗}-weak type

References

• Bernal , L. : Orden relative de crecimiento de funciones enteras , Collect.Math., Vol. 39(1988), pp.209-229.
• Datta, S. K., Biswas, T. and Sen, P.: Measure of growth of entire functions using relative L^{∗} order, International Journal of Mathematical Science and Engineering Applications (IJMSEA), Vol. 8, No. IV (July, 2014), pp. 125-133.
• Datta, S. K, Biswas, T. and Dutta, D. : Generalized relative type and Generalized relative weak type of entire function, Journal of Complex Analysis, Volume 2016, Article ID 3468354, 1 pages, http://ds.doi.org/10.1155/20163468354.
• Datta, S. K, Biswas : Measure of growths of entire functions from the view point of their relative L^{∗}-type and relative L^{∗}-weak type, Palestine Journal of Mathematics; Vol 6 (special Issue: II), pp. 149-156.
• Datta , S. K. and Biswas, T. : Growth of entire functions based on relative order, International Journal of Pure and Applied Mathematics (IJPAM), Vol.51, No.1 (2009), pp. 49-58.
• Datta , S. K. and Jha, A. : On the weak type of meromorphic functions, Int. Math. Forum, Vol. 4, No. 12 (2009), pp. 569-579.
• Datta , S. K. and Kar, S. : On the L-order of meromorphic functions based on relative sharing, International Journal of Pure and Applied Mathematics (IJPAM), Vol.56, No.1 (2009), pp. 43-47.
• Singh, S. K. and Barker, G. P. : Slowly changing functions and their applications, Indian J. Math., Vol. 19 , No. 1(1977), pp 1-6.
• 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( March 1988) , pp. 284-293.
• Valiron, G. : Lectures on the General Theory of Integral Functions, Chelsea Publishing Company,1949.