Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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SLOWLY CHANGING FUNCTION ORIENTED GROWTH MEASUREMENT OF DIFFERENTIAL POLYNOMIAL AND DIFFERENTIAL MONOMIAL

  • Received : 2018.05.23
  • Accepted : 2019.01.22
  • Published : 2019.03.30
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Abstract

In the paper we establish some new results depending on the comparative growth properties of composite entire and meromorphic functions using relative $_pL^*$-order, relative $_pL^*$-lower order and differential monomials, differential polynomials generated by one of the factors.

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References

  1. N. Bhattacharjee and I. Lahiri, Growth and value distribution of differential polynomials, Bull. Math. Soc. Sci. Math. Roum., Nouv. Ser. 39 (1996), 85-104.
  2. T. Biswas, Comparative growth measurement of differential monomials and differential polynomials depending upon their relative $_pL^{\ast}$-types and relative $_pL^{\ast}$-weak types, Aligarh Bull. Math. 36 (2017), 73-94.
  3. T. Biswas, Comparative growth analysis of differential monomials and differential polynomials depending on their relative $_pL^{\ast}$-orders, J. Chungcheong Math. Soc. 31 (2018), 103-130. https://doi.org/10.14403/JCMS.2018.31.1.103
  4. T. Biswas, Advancement on the study of growth analysis of differential polynomial and differential monomial in the light of slowly increasing functions, Carpathian Math. Publ. 10 (2018), 31-57. https://doi.org/10.15330/cmp.10.1.31-57
  5. W. Bergweiler, On the Nevanlinna Characteristic of a composite function, Complex Variables Theory Appl. 10 (1988), 225-236. https://doi.org/10.1080/17476938808814301
  6. L. Bernal, Orden relative de crecimiento de funciones enteras, Collect. Math., 39 (1988), 209-229.
  7. W. Doeringer, Exceptional values of differential polynomials, Pacific J. Math., 98 (1982), 55-62. https://doi.org/10.2140/pjm.1982.98.55
  8. 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 (2014), 207-218.
  9. W.K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  10. I. Lahiri, Deficiencies of differential polynomials, Indian J. Pure Appl. Math., 30 (1999), 435-447.
  11. I. Laine, Nevanlinna Theory and Complex Di erential Equations. De Gruyter, Berlin, 1993.
  12. B. K. Lahiri and D. Banerjee, Relative order of entire and meromorphic functions, Proc. Nat. Acad. Sci. India Ser. A., 69(A) (1999), 339-354.
  13. K. Niino and C.C. Yang, Some growth relationships on factors of two composite entire functions, Factorization theory of meromorphic functions and related topics, Marcel Dekker, Inc.(New York and Basel), 1982, 95-99.
  14. D. Somasundaram and R. Thamizharasi, A note on the entire functions of L-bounded index and L-type, Indian J. Pure Appl. Math., 19 (1988), 284-293:
  15. L.R. Sons, Deficiencies of monomials, Math.Z, 111 (1969), 53-68. https://doi.org/10.1007/BF01110917
  16. G. Valiron, Lectures on the general theory of integral functions, Chelsea Publishing Company, 1949.
  17. L. Yang, Value distribution theory and new research on it, Science Press, Beijing, 1982.
  18. H. X. Yi, On a result of Singh, Bull. Austral. Math. Soc., 41 (1990), 417-420. https://doi.org/10.1017/S0004972700018293
  19. C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
  20. L. Yang, Value distribution theory, Springer-Verlag, Berlin, 1993.