Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SOME RESULTS RELATING TO SUM AND PRODUCT THEOREMS OF RELATIVE (p, q, t) L-TH ORDER AND RELATIVE (p, q, t) L-TH TYPE OF ENTIRE FUNCTIONS

  • Received : 2018.03.05
  • Accepted : 2018.03.18
  • Published : 2018.06.30
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Abstract

Orders and types of entire functions have been actively investigated by many authors. In this paper, we investigate some basic properties in connection with sum and product of relative (p, q, t) L-th order, relative (p, q, t) L-th type, and relative (p, q, t) L-th weak type of entire functions with respect to another entire function where $p,q{\in}{\mathbb{N}}$ and $t{\in}{\mathbb{N}}{\cup}\{-1,0\}$.

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References

  1. L. Bernal, Crecimiento relativo de funciones enteras. Contribuci on al estudio de lasfunciones enteras con indice 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. S. K. Datta, T. Biswas and P. Sen, Growth of entire functions from the view point of relative L*-order, J. Adv. Res. Appl. Math. 7 (1) (2015), 74-93, doi: 10.5373/jaram.2072.062914.
  4. S. K. Datta, T. Biswas and A. Hoque, On sum and product theorems related to relative L*-type and relative L*-weak type of entire functions, J. Class. Anal. 8 (1) (2016), 1-30, doi:10.7153/jca-08-01.
  5. W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  6. O. P. Juneja, G. P. Kapoor and 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. O. P. Juneja, G. P. Kapoor and S. K. Bajpai, On the (p; q)-type and lower (p; q)-type of an entire function, J. Reine Angew. Math. 290 (1977), 180-190.
  8. L. M. Sanchez Ruiz, S. K. Datta, T. Biswas and G. K. Mondal, On the (p; q)-th relative order oriented growth properties of entire functions, Abstr. Appl. Anal. 2014, Article ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
  9. 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
  10. D. Somasundaram and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl.Math., 19 (3) (1988), 284-293.
  11. E. C. Titchmarsh, The theory of functions, 2nd ed. Oxford University Press, Oxford, 1968.
  12. G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.