COMPARATIVE GROWTH ANALYSIS OF SPECIAL TYPE OF
DIFFERENTIAL POLYNOMIAL GENERATED BY ENTIRE
AND MEROMORPHIC FUNCTIONS ON THE BASIS
OF THEIR (p,q)-th ORDER

Abstract

In this paper we aim to establish some results depending on the comparative growth properties of composite transcendental entire or meromorphic functions and some special type of differential polynomials generated by one of the factors on the basis of (p,q)-th order and (p,q)-th lower order where p,q are positive integers with p≥ q.

Citation details of the article



Journal: International Journal of Applied Mathematics
Journal ISSN (Print): ISSN 1311-1728
Journal ISSN (Electronic): ISSN 1314-8060
Volume: 31
Issue: 1
Year: 2018

DOI: 10.12732/ijam.v31i1.7

Download Section



Download the full text of article from here.

You will need Adobe Acrobat reader. For more information and free download of the reader, please follow this link.

References

  1. [1]W. Bergweiler, On the Nevanlinna Characteristic of a composite function, Complex Variables Theory Appl., 10, No 2-3 (1988), 225-236.
  2. [2] W. Bergweiler, On the growth rate of composite meromorphic functions, Complex Variables Theory Appl., 14, No 1-4 (1990), 187-196.
  3. [3] S.S. Bhooshnurmath, K.S.L.N. Prasad, The value distribution of some differential polynomials, Bull. Cal. Math. Soc., 101, No 1 (2009), 55-62.
  4. [4] S.K. Datta, T. Biswas, Growth rates of composite entire and meromorphic functions, Bull. Allahabad Math. Soc., 27 (2012), 55-94.
  5. [5] W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  6. [6] O.P. Juneja, G.P. Kapoor, 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.
  7. [7] Q. Lin, C. Dai, On a conjecture of Shah concerning small functions, Kexue Tong bao (English Ed.), 31, No 4 (1986), 220-224.
  8. [8] I. Lahiri, Generalised proximate order of meromorphic functions, Mat. Vesnik, 41 (1989), 9-16.
  9. [9] I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin (1993).
  10. [10] D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc., 69 (1963), 411-414.
  11. [11] C.C. Yang, H.X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht (2003).
  12. [12] L. Yang, Value Distribution Theory, Springer-Verlag, Berlin (1993).
  13. [13] G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company (1949).