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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

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.




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

Abstract

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.
There are 16 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Sanjib Kumar Datta

Tanmay Biswas This is me

Jinarul Haque Shaikh This is me

Publication Date September 30, 2016
Published in Issue Year 2016 Volume: 4 Issue: 3

Cite

APA Datta, S. K., Biswas, T., & Shaikh, J. H. (2016). Estimation of growths of composite entire and meromorphic functions using their generalized relative orders. New Trends in Mathematical Sciences, 4(3), 186-196.
AMA Datta SK, Biswas T, Shaikh JH. Estimation of growths of composite entire and meromorphic functions using their generalized relative orders. New Trends in Mathematical Sciences. September 2016;4(3):186-196.
Chicago Datta, Sanjib Kumar, Tanmay Biswas, and Jinarul Haque Shaikh. “Estimation of Growths of Composite Entire and Meromorphic Functions Using Their Generalized Relative Orders”. New Trends in Mathematical Sciences 4, no. 3 (September 2016): 186-96.
EndNote Datta SK, Biswas T, Shaikh JH (September 1, 2016) Estimation of growths of composite entire and meromorphic functions using their generalized relative orders. New Trends in Mathematical Sciences 4 3 186–196.
IEEE S. K. Datta, T. Biswas, and J. H. Shaikh, “Estimation of growths of composite entire and meromorphic functions using their generalized relative orders”, New Trends in Mathematical Sciences, vol. 4, no. 3, pp. 186–196, 2016.
ISNAD Datta, Sanjib Kumar et al. “Estimation of Growths of Composite Entire and Meromorphic Functions Using Their Generalized Relative Orders”. New Trends in Mathematical Sciences 4/3 (September 2016), 186-196.
JAMA Datta SK, Biswas T, Shaikh JH. Estimation of growths of composite entire and meromorphic functions using their generalized relative orders. New Trends in Mathematical Sciences. 2016;4:186–196.
MLA Datta, Sanjib Kumar et al. “Estimation of Growths of Composite Entire and Meromorphic Functions Using Their Generalized Relative Orders”. New Trends in Mathematical Sciences, vol. 4, no. 3, 2016, pp. 186-9.
Vancouver Datta SK, Biswas T, Shaikh JH. Estimation of growths of composite entire and meromorphic functions using their generalized relative orders. New Trends in Mathematical Sciences. 2016;4(3):186-9.