TITLE

Uniqueness of Entire Functions Sharing Polynomials with Their Derivatives

AUTHOR(S)
Jianming Qi; Feng Lü; Ang Chen
PUB. DATE
January 2009
SOURCE
Abstract & Applied Analysis;2009, Special section p1
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We use the theory of normal families to prove the following. Let Q1(z) = a1zp +a1,p-1zp-1 +・ ・ ・+ a1,0 and Q2(z) = a2zp + a2,p-1zp-1 + ・ ・ ・ + a2,0 be two polynomials such that degQ1 = degQ2 = p (where p is a nonnegative integer) and a1, a2(a2≠ 0) are two distinct complex numbers. Let f(z) be a transcendental entire function. If f(z) and f'(z) share the polynomial Q1(z) CM and if f(z) = Q2(z) whenever f'(z) = Q2(z), then f ≡ f'. This result improves a result due to Li and Yi.
ACCESSION #
55252839

 

Related Articles

  • On Uniqueness Theorems of Meromorphic Functions Concerning Weighted Sharing of Three Values. Xiao-Min Li; Hong-Xun Yi // Bulletin of the Malaysian Mathematical Sciences Society;2010, Vol. 33 Issue 1, p1 

    In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain a uniqueness theorem which improves those given by Ozawa, H. X. Yi, I. Lahiri, Q. C. Zhang, and others. Some examples are provided to show that the results in this paper are the...

  • Some Further Results on Weighted Sharing of Values for Meromorphic Functions Concerning a Result of Terglane. Xiao-Min Li; Hong-Xun Yi // Kyungpook Mathematical Journal;2008, Vol. 48 Issue 3, p419 

    In this paper, we deal with the problem of meromorphic functions that have three weighted sharing values, and obtain some uniqueness theorems which improve those given by N. Terglane, Hong-Xun Yi & Xiao-Min Li, and others. Some examples are provided to show that the results in this paper are...

  • ON UNICITY OF MEROMORPHIC FUNCTIONS DUE TO A RESULT OF YANG - HUA. Xiao-Tian Bai; Qi Han // Archivum Mathematicum;2007, Vol. 43 Issue 2, p93 

    This paper studies the unicity of meromorphic(resp. entire) functions of the form fnfl and obtains the following main result: Let f and g be two non-constant meromorphic (reap. entire) functions, and let a ? C\{0} be a non-zero finite value. Then, the condition that E3)(a, fnfl) = E3)(a, gngl)...

  • THE GROWTH AND SINGULAR DIRECTION OF ALGEBROID FUNCTIONS. Songmin Wang // Annales Academiae Scientiarum Fennicae. Mathematica;2012, Vol. 37 Issue 2, p479 

    In this paper, we obtain a basic inequation, investigate the relation between the growth as well as the singular direction of algebroid functions and those of their coefficients, and give some applications of the results.

  • Meromorphic Function that Shares One Small Function with its Differential Polynomial.  // Kyungpook Mathematical Journal;Sep2010, Vol. 50 Issue 3, p447 

    No abstract available.

  • ON ROOTS OF POLYNOMIALS WITH POSITIVE COEFFICIENTS. Zaïmi, Toufik // Publications de l'Institut Mathematique;2011, Vol. 89 Issue 103, p89 

    No abstract available.

  • Uniqueness of Meromorphic Functions and Differential Polynomials. Jin-Dong Li // International Journal of Mathematics & Mathematical Sciences;2011, p1 

    We study the uniqueness of meromorphic functions and differential polynomials sharing one value with weight and prove two main theorems which generalize and improve some results earlier given by M. L. Fang, S. S. Bhoosnurmath and R. S. Dyavanal, and so forth.

  • Certain Nonlinear Differential Polynomials Sharing a Nonzero Polynomial with Finite Weight. BANERJEE, ABHIJIT; SAHOO, PULAK // Kyungpook Mathematical Journal;Sep2015, Vol. 55 Issue 3, p653 

    With the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. Our results improve some recent results including that of a present first author [Kyungpook Math. J., 51(2011), 43-58].

  • Unicity of Meromorphic Function and its Derivative. Ang Chen; Guowei Zhang // Kyungpook Mathematical Journal;Mar2010, Vol. 50 Issue 1, p71 

    In this paper, we deal with the uniqueness problems of meromorphic functions that share a small function with its derivative and improve some results of Yang, Yu, Lahiri, and Zhang, also answer some questions of T. D. Zhang and W. R. Lü.

Share

Read the Article

Courtesy of VIRGINIA BEACH PUBLIC LIBRARY AND SYSTEM

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics