Estimation of growths of composite entire and meromorphic functions using their generalized relative orders

Year 2016, Volume: 4 Issue: 3, 186 - 196, 30.09.2016

Sanjib Kumar Datta , Tanmay Biswas Jinarul Haque Shaikh

https://izlik.org/JA72WU23SF

Abstract

In this paper
we establish some newly developed results related to the growth rates of
composite entire and meromorphic functions on the basis of their generalized
relative orders and generalized relative lower orders.

Keywords

Entire function , meromorphic function , generalized order (generalized lower order) , generalized relative order (generalized relative lower order) , Property (A)

References

• L. Bernal : Crecimiento relativo de funciones enteras. Contribución al estudio de lasfunciones enteras con13 ̆053'fndice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
• L. Bernal : Orden relative de crecimiento de funciones enteras, Collect. Math., Vol. 39 (1988), pp.209-229.
• W. Bergweiler : On the Nevanlinna characteristic of a composite function, Complex Variables, Vol. 10 (1988), pp. 225-236.
• W. Bergweiler : On the growth rate of composite meromorphic functions, Complex Variables, Vol. 14 (1990), pp. 187-196.
• D. Banerjee and S. Jana : Meromorphic functions of relative order (p,q), Soochow Journal of Mathematics, Vol. 33, No. 3 (July, 2007), pp. 343-357.
• S. K. Datta and T. Biswas : Growth of entire functions based on relative order, Int. J. Pure Appl. Math., Vol. 51, No. 1 (2009), pp. 49-58.
• S. K. Datta and T. Biswas : Relative order of composite entire functions and some related growth properties, Bull. Cal. Math. Soc., Vol.102, No.3 (2010) pp.259-266.
• 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), Vol. 7, No. II (March, 2013), pp. 59-67.
• S. K. Datta , T. Biswas and R. Biswas : Comparative growth properties of composite entire functions in the light of their relative order, The Mathematics Student, Vol. 82, No. 1-4 (2013), pp. 209-216.
• S. K. Datta, T. Biswas and C. Biswas: Growth analysis of composite entire and meromorphic functions in the light of their relative orders, International Scholarly Research Notices, Volume 2014, Article ID538327, 6 pages; http://dx.doi.org/10.1155/2014/538327.
• S. K. Datta, T. Biswas and C. Biswas: Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, International J. of Math. Sci. & Engg. Appls. (IJMSEA), Vol. 8 No. IV (July, 2014), pp. 207-218.
• W. K. Hayman : Meromorphic Functions, The Clarendon Press, Oxford (1964).
• B. K. Lahiri and D. Banerjee : Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., Vol. 69(A), No. 3, (1999), pp.339-354.
• D. Sato : On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., Vol. 69 (1963), pp. 411-414.
• E. C. Titchmarsh : The theory of functions, 2nd edition, Oxford University Press, Oxford, 1939.
• G. Valiron : Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.