Further study on the results of Sheremeta

In this paper we estimate some growth rates of composite entire and meromorphic functions in the light of their relative (p,q)-th order and relative (p,q)-th lower order which considerably extend some results of Sheremeta [14].

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  • Bernal, L., Crecimiento relativo de funciones enteras. Contribuci´on al estudio de lasfunciones enteras con ´ındice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
  • Bernal, L., Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209-229.
  • Bergweiler, W., On the Nevanlinna Characteristic of a composite function, Complex Variables Theory Appl. , 10 (2-3) (1988), 225-236.
  • Bergweiler, W., On the growth rate of composite meromorphic functions, Complex Variables Theory Appl. , 14 (1-4) (1990), 187-196.
  • Clunie, J., The composition of entire and meromorphic functions, In: Mathematical essays dedicated to A.J.Macintyre, Ohio University Press, (1970), 75 - 92.
  • Debnath, L., Datta, S. K., Biswas T. and Kar, A., Growth of meromorphic functions depending on (p,q)-th relative order, Facta Univ. Ser. Math. Inform., 31 (3) (2016), 691-705.
  • Datta, S. K., Biswas T. and Biswas, C., Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg. Appls. (IJMSEA), 8 (IV) (2014), 207-218.
  • Hayman, W.K., Meromorphic Functions, The Clarendon Press, Oxford (1964).
  • 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., 282, (1976), 53-67.
  • Laine, I., Nevanlinna Theory and Complex Differential Equations. De Gruyter, Berlin, 1993.
  • Lahiri B. K. and Banerjee, D., Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., 69(A) (3) (1999), 339-354.
  • Ruiz, L. M. S., Datta, S. K., Biswas T. and Mondal, G. K., On the (p,q)-th relative order oriented growth properties of entire functions, Abstr. Appl. Anal., 2014, Art. ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
  • Sato, D., On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411-414.
  • Sheremeta, M. M., On the growth of a composite entire functions, Carpathian Math. Publ.,9 (2) (2017), 181--187.
  • Titchmarsh, E. C., The Theory of Functions, 2nd ed. Oxford University Press, Oxford , (1968).
  • Yang C. C. and Yi, H. X., Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
  • Yang, L., Value distribution theory, Springer-Verlag, Berlin, 1993.
  • Valiron, G., Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.