Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

GENERALIZED RELATIVE ORDER-DEPENDENT GROWTHS OF COMPOSITE ENTIRE FUNCTIONS

  • Received : 2016.07.31
  • Accepted : 2016.09.26
  • Published : 2017.07.31
Download PDF
⟨ Previous Next ⟩

Abstract

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

Keywords

References

  1. L. Bernal, Crecimiento relativo de funciones enteras, Contribucion al estudio de lasfunciones enteras conindice exponencial finito, Doctoral Dissertation, University of Seville, Spain, 1984.
  2. L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math. 39 (1988), 209-229.
  3. J. Clunie, The composition of entire and meromorphic functions, Mathematical Essays Dedicated to A. J. Macintyre, pp. 7592, Ohio Univ. Press, Athens, Ohio, 1970.
  4. S. K. Datta and T. Biswas, Growth of entire functions based on relative order, Int. J. Pure Appl. Math. 51 (2009), no. 1, 49-58.
  5. S. K. Datta and T. Biswas, Relative order of composite entire functions and some related growth properties, Bull. Calcutta Math. Soc. 102 (2010), no. 3, 259-266.
  6. S. K. Datta, T. Biswas, and R. Biswas, On relative order based growth estimates of entire functions, International J. Math. Sci. Engg. Appls. (IJMSEA) 7 (2013), no. 2, 59-67.
  7. 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 (2013), no. 1-4, 1-8.
  8. S. K. Datta, T. Biswas, and C. Ghosh, Growth analysis of entire functions concerning generalized relative type and generalized relative weak type, Facta Univ. Ser. Math. Inform. 30 (2015), no. 3, 295-324.
  9. S. K. Datta, T. Biswas, and D. C. Pramanik, On relative order and maximum term - related comparative growth rates of entire functions, J. Tripura Math. Soc. 14 (2012), 60-68.
  10. S. K. Datta and A. R. Maji, Relative order of entire functions in terms of their maximum terms, Int. J. Math. Analy. 5 (2011), no. 41-44, 2119-2126.
  11. B. K. Lahiri and D. Banerjee, Generalised relative order of entire functions, Proc. Nat. Acad. Sci. India 72(A) (2002), no. 4, 351-271.
  12. D. Sato, On the rate of growth of entire functions of fast growth, Bull. Amer. Math. Soc. 69 (1963), 411-414. https://doi.org/10.1090/S0002-9904-1963-10951-9
  13. A. P. Singh, On maximum term of composition of entire functions, Proc. Nat. Acad. Sci. India Sect. A 59 (1989), no. 1, 103-115.
  14. 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 (1991), no. 12, 1019-1026.
  15. E. C. Titchmarsh, The Theory of Functions, 2nd ed. Oxford University Press, Oxford, 1968.
  16. G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Publishing Company, 1949.