Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

AN ENTIRE FUNCTION SHARING A POLYNOMIAL WITH LINEAR DIFFERENTIAL POLYNOMIALS

  • Ghosh, Goutam Kumar (Department of Mathematics Dr. Bhupendra Nath Dutta Smriti Mahavidyalaya(The University of Burdwan))
  • Received : 2017.04.22
  • Accepted : 2018.03.29
  • Published : 2018.04.30
Download PDF
⟨ Previous Next ⟩

Abstract

The uniqueness problems on entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results on this topic have been obtained. In this paper, we study an entire function f(z) that shares a nonzero polynomial a(z) with $f^{(1)}(z)$, together with its linear differential polynomials of the form: $L=L(f)=a_1(z)f^{(1)}(z)+a_2(z)f^{(2)}(z)+{\cdots}+a_n(z)f^{(n)}(z)$, where the coefficients $a_k(z)(k=1,2,{\ldots},n)$ are rational functions and $a_n(z){\not{\equiv}}0$.

Keywords

References

  1. J. Chang and M. Fang, Entire functions that share a small function with their derivatives, Complex Var. Theory Appl. 49 (2004), no. 12, 871-895.
  2. W. K. Hayman, Meromorphic Functions, Oxford Math. Monogr., Clarendon Press, Oxford, 1964.
  3. G. Jank, E. Mues, and L. Volkmann, Meromorphe Funktionen, die mit ihrer ersten und zweiten Ableitung einen endlichen Wert teilen, Complex Variables Theory Appl. 6 (1986), no. 1, 51-71. https://doi.org/10.1080/17476938608814158
  4. I. Lahiri and G. K. Ghosh, Entire functions sharing values with their derivatives, Analysis (Munich) 31 (2011), no. 1, 47-59.
  5. P. Li, Entire functions that share one value with their linear differential polynomials, Kodai Math. J. 22 (1999), no. 3, 446-457. https://doi.org/10.2996/kmj/1138044096
  6. A. Z. Mohonko, The Nevanlinna characteristics of certain meromorphic functions, Teor. Funkcii Funkcional. Anal. i Prilozen. No. 14 (1971), 83-87.
  7. E. Mues and N. Steinmetz, Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen, Manuscripta Math. 29 (1979), no. 2-4, 195-206. https://doi.org/10.1007/BF01303627
  8. L. A. Rubel and C. C. Yang, Values shared by an entire function and its derivative, in Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), 101-103. Lecture Notes in Math., 599, Springer, Berlin, 1977.
  9. G. Valiron, Lectures on General Theory of Integral Functions, Edouard Privat, Toulouse, 1923.
  10. C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557, Kluwer Academic Publishers Group, Dordrecht, 2003.
  11. H. L. Zhong, Entire functions that share one value with their derivatives, Kodai Math. J. 18 (1995), no. 2, 250-259. https://doi.org/10.2996/kmj/1138043421