Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Mathematica Slovaca

Editor-in-Chief: Pulmannová, Sylvia

IMPACT FACTOR 2018: 0.490

CiteScore 2018: 0.47

SCImago Journal Rank (SJR) 2018: 0.279
Source Normalized Impact per Paper (SNIP) 2018: 0.627

Mathematical Citation Quotient (MCQ) 2018: 0.29

See all formats and pricing
More options …
Volume 64, Issue 5


Some results on the entire function sharing problem

BaoQin Chen / Sheng Li
Published Online: 2014-11-15 | DOI: https://doi.org/10.2478/s12175-014-0270-2


Our main result is as follows: let f and a be two entire functions such that $$\max \{ \rho _2 (f),\rho _2 (a)\} < \tfrac{1} {2}$$. If f and f (k) a CM, and if ρ(a (k) − a) < ρ(f − a), then f (k) − a = c(f − a) for some nonzero constant c. This result is applied to improve a result of Gundersen and Yang.

MSC: Primary 30D35

Keywords: entire function; shared value; derivative

  • [1] BARRY, P. D.: On a theorem of Besicovitch, Q. J. Math. 14 (1963), 293–302. http://dx.doi.org/10.1093/qmath/14.1.293CrossrefGoogle Scholar

  • [2] BRÜCK, R.: On entire functions which share one value CM with their first derevative, Results Math. 30 (1996), 21–24. http://dx.doi.org/10.1007/BF03322176CrossrefGoogle Scholar

  • [3] CHANG, J. M.— ZHU, Y. Z.: Entire functions that share a small function with their derivatives, J. Math. Anal. Appl. 351 (2009), 491–496. http://dx.doi.org/10.1016/j.jmaa.2008.07.080CrossrefGoogle Scholar

  • [4] CHEN, Z. X.: The growth of solutions of f″ + e−z f′+Q(z)f = 0 where the order of Q =1, Sci. China Math. Ser. A 45 (2002), 290–300. Google Scholar

  • [5] CHEN, Z. X.— SHON, K. H.: On conjecture of R. Brück concernig the entire function sharing one value CM with its derivative, Taiwanese J. Math. 8 (2004), 235–244. Google Scholar

  • [6] CHEN, Z. X.— SHON, K. H.: On the entire function sharing one value CM with k-th derivatives, J. Korean Math. Soc. 42 (2005), 85–99. http://dx.doi.org/10.4134/JKMS.2005.42.1.085CrossrefGoogle Scholar

  • [7] CHEN, Z. X.— YANG, C. C.: Some further results on the zeros and growths of entire solutions of second order linear differential equations, KodaiMath. J. 22 (1999), 273–285. Google Scholar

  • [8] CONWAY, J. B.: Functions of One Complex Variable (2nd ed.), Spring-Verlag, World Pulishing Corporation, Beijing, 2004. Google Scholar

  • [9] HAYMAN, W. K.: Meromorphic Function, Clarendon Press, Oxford, 1964. Google Scholar

  • [10] GUNDERSEN, G. G.: Estimates for the logarithmic derivative of a meromorphic function, plus similar estimates, J. Lond. Math. Soc. (2) 37 (1988), 88–104. Google Scholar

  • [11] GUNDERSEN, G. G.— YANG, L. Z.: Entire functions that share one value with one or two of their derivatives, J. Math. Anal. Appl. 223 (1998), 88–95. http://dx.doi.org/10.1006/jmaa.1998.5959CrossrefGoogle Scholar

  • [12] LAINE, I.: Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin, 1993. http://dx.doi.org/10.1515/9783110863147CrossrefGoogle Scholar

  • [13] JANK, G.— VOLKMANN, L.: Meromorphe Funktionen und Differentialgleichungen, Birkhäuser, Basel-Boston, 1985. Google Scholar

  • [14] MARKUSHEVICH, A. I.: Theory of Functions of a Complex Variable, Vol. II, Prentice-Hall, Englewood Cliffs, NJ, 1965. Google Scholar

  • [15] RUBEL, L. A.— YANG, C. C.: Values shared by an entire function and its derivative. In: Lecture Notes in Math. 599, Springer-Verlag, Berlin, 1977, 101–103. Google Scholar

  • [16] YANG, C. C.— YI, H. X.: Uniqueness Theory of Meromorphic Functions, Kluwer Academic publishers, Dordrecht, 2003. http://dx.doi.org/10.1007/978-94-017-3626-8CrossrefGoogle Scholar

About the article

Published Online: 2014-11-15

Published in Print: 2014-10-01

Citation Information: Mathematica Slovaca, Volume 64, Issue 5, Pages 1217–1226, ISSN (Online) 1337-2211, ISSN (Print) 0139-9918, DOI: https://doi.org/10.2478/s12175-014-0270-2.

Export Citation

© 2014 Mathematical Institute, Slovak Academy of Sciences. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in