Korean J. Math. Vol. 26 No. 3 (2018) pp.405-424
DOI: https://doi.org/10.11568/kjm.2018.26.3.405

Growth analysis of composite entire functions from the view point of relative $(p,q)$-th order

Main Article Content

Tanmay Biswas


In this paper we study some comparative growth properties of composite entire functions on the basis of relative $\left( p,q\right) $-th order and relative $\left( p,q\right) $-th lower order of entire function with respect to another entire function where $p$ and $q$ are any two positive integers.

Article Details


[1] L. Bernal, Crecimiento relativo de funciones enteras, Contribucion al estudio de lasfunciones enteras conındice exponencial finito, Doctoral Dissertation, Univer- sity of Seville, Spain, 1984. Google Scholar

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

[3] J. Clunie, The composition of entire and meromorphic functions, Mathematical Essays dedicated to A. J. Macintyre,Ohio University Press (1970), 75–92. Google Scholar

[4] S. K. Datta and T. Biswas, Growth of entire functions based on relative order, Int. J. Pure Appl. Math. 51 (1) (2009), 49–58. Google Scholar

[5] S. K. Datta and T. Biswas, Relative order of composite entire functions and some related growth properties, Bull. Cal. Math. Soc. 102 (3) (2010), 259–266. Google Scholar

[6] S. K. Datta and A. R. Maji, Relative order of entire functions in terms of their maximum terms, Int. Journal of Math. Analysis. 5 (43) (2011), 2119–2126. Google Scholar

[7] S. K. Datta, T. Biswas and D. C. Pramanik, On relative order and maximum term -related comparative growth rates of entire functions, Journal of Tripura Mathematical Society. 14 (2012), 60–68 Google Scholar

[8] S. K. Datta , T. Biswas and R. Biswas, On relative order based growth estimates of entire functions, International J. of Math. Sci. & Engg. Appls. (IJMSEA). 7 (II) (2013), 59–67. Google Scholar

[9] S. K. Datta , T. Biswas and R. Biswas, Comparative growth properties of composite entire functions in the light of their relative order, Math. Student. 82 (1-4) (2013), 209–216. Google Scholar

[10] O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p,q)-order and lower (p,q)-order of an entire function, J. Reine Angew. Math. 282 (1976), 53–67. Google Scholar

[11] B. K. Lahiri and D. Banerjee, Entire functions of relative order (p, q), Soochow J. Math. 31 (4) (2005), 497–513. Google Scholar

[12] L. M. S. Ruiz, S. K. Datta,T. Biswas,and G. K.Mondal, On the (p,q) th relative order oriented growth properties of entire functions, Abstract and Applied Analysis,Hindawi Publishing Corporation, Volume 2014, Article ID 826137, 8 pages. Google Scholar

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

[14] A. P. Singh, On maximum term of composition of entire functions, Proc. Nat. Acad. Sci. India, 59 (A), Part I (1989), 103–115. Google Scholar

[15] A. P. Singh and M. S. Baloria, On the maximum modulus and maximum term of composition of entire functions, Indian J. Pure Appl. Math. 22 (12) (1991), 1019–1026. Google Scholar

[16] E. C. Titchmarsh, The theory of functions , 2nd ed. Oxford University Press, Oxford , 1968. Google Scholar

[17] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Pub- lishing Company, 1949. Google Scholar