Korean Journal of Mathematics

  • 제27권4호
  • /
  • Pages.899-927
  • /
  • 2019
  • /
  • 1976-8605(pISSN)
  • /
  • 2288-1433(eISSN)
강원경기수학회 (The Kangwon-Kyungki Mathematical Society)
권호 표지
DOI QR코드

DOI QR Code

SOME GROWTH ASPECTS OF SPECIAL TYPE OF DIFFERENTIAL POLYNOMIAL GENERATED BY ENTIRE AND MEROMORPHIC FUNCTIONS ON THE BASIS OF THEIR RELATIVE (p, q)-TH ORDERS

  • 투고 : 2019.04.27
  • 심사 : 2019.10.16
  • 발행 : 2019.12.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In this paper we establish some results depending on the comparative growth properties of composite entire and meromorphic functions using relative (p, q)-th order and relative (p, q)-th lower order where p, q are any two positive integers and that of a special type of differential polynomial generated by one of the factors.

키워드

과제정보

The author is extremely grateful to the anonymous learned referee for his keen reading, valuable suggestion and constructive comments for the improvement of the paper.

참고문헌

  1. L. Bernal-Gonzalez, Crecimiento relativo de funciones enteras. Aportaciones al estudio de las funciones enteras con indice exponencial finito, Doctoral Thesis, 1984, Universidad de Sevilla, Spain.
  2. L. Bernal, Orden relative de crecimiento de funciones enteras , Collect. Math., 39 (1988), 209-229.
  3. W. Bergweiler, On the Nevanlinna characteristic of a composite function, Complex Variables Theory Appl. 10 (2-3) (1988), 225-236. https://doi.org/10.1080/17476938808814301
  4. W. Bergweiler, On the growth rate of composite meromorphic functions, Complex Variables Theory Appl. 14 (1-4) (1990), 187-196. https://doi.org/10.1080/17476939008814417
  5. S. S. Bhooshnurmath and K. S. L. N. Prasad, The value distribution of some differental polynomials, Bull. Cal. Math. Soc 101 (1) (2009), 55-62.
  6. L. Debnath, S. K. Datta, T. Biswas and A. Kar, Growth of meromorphic functions depending on (p,q)-th relative order, Facta Univ. Ser. Math. Inform. 31 (3) (2016), 691-705.
  7. S. K. Datta, T. Biswas and C. Biswas, Measure of growth ratios of composite entire and meromorphic functions with a focus on relative order, Int. J. Math. Sci. Eng. Appl. 8 (IV) (July, 2014), 207-218.
  8. W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  9. 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.
  10. 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.
  11. I. Laine, Nevanlinna Theory and Complex Differential Equations, De Gruyter, Berlin, 1993.
  12. L. M. S. Ruiz, S. K. Datta, T. Biswas and G. K. Mondal, On the (p,q)-th relative order oriented growth properties of entire functions, Abstract and Applied Analysis, Vol.2014, Article ID 826137, 8 pages, http://dx.doi.org/10.1155/2014/826137.
  13. X. Shen, J. Tu and H. Y. Xu, Complex oscillation of a second-order linear differential equation with entire coefficients of [p; q]-$\varphi$ order, Adv. Difference Equ. 2014,2014: 200, 14 pages, http://www.advancesindifferenceequations.com/content/2014/1/200.
  14. 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
  15. C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
  16. L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993.
  17. G. Valiron, Lectures on the General Theory of Integral Functions, Chelsea Pub-lishing Company, (1949).