On an open problem of Xiao-Bin Zhang and Jun-Feng Xu

• Autorzy: Majumder S.
• Języki publikacji: EN

Abstrakty

EN

The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].

Słowa kluczowe

EN

uniqueness; meromorphic function; small functions; nonlinear differential polynomials

PL

wyjątkowość; funkcja meromorficzna; funkcja mała; wielomian różniczkowy nieliniowy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2016
• Tom: Vol. 49, nr 2
• Strony: 161--182
• Opis fizyczny: Bibliogr. 19 poz.

Twórcy

autor

Majumder S.

• Department of Mathematics Katwa College Katwa, West Bengal-713130, India

Bibliografia

• [1] A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci. 22 (2005), 3587–3598.
• [2] A. Banerjee, Uniqueness of certain nonlinear differential polynomials sharing 1-points, Kyungpook Math. J. 51 (2011), 43–58.
• [3] M. L. Fang, H. L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl. 268 (2002), 426–439.
• [4] G. Frank, Eine Vermutung Von Hayman über Nullslellen meromorphic Funktion, Math. Z. 149 (1976), 29–36.
• [5] W. K. Hayman, Picard values of meromorphic functions and their derivatives, Ann. of Math. 70 (1959), 9–42.
• [6] W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
• [7] I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci. 28 (2001), 83–91.
• [8] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206.
• [9] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), 241–253.
• [10] I. Lahiri, A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), 79–87.
• [11] I. Lahiri, S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), 95–100.
• [12] J. F. Xu, F. Lu, H. X. Yi, Fixed points and uniqueness of meromorphic functions, Comput. Math. Appl. 59 (2010), 9–17.
• [13] C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107–112.
• [14] C. C. Yang, X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395–406.
• [15] C. C. Yang, H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
• [16] H. X. Yi, Meromorphic functions that share three sets, Kodai Math. J. 20 (1997), 22–32.
• [17] H. X. Yi, Meromorphic functions that share one or two values II, Kodai Math. J. 22 (1999), 264–272.
• [18] Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6(4) (2005), Art. 116 [online: http://jipam.vu.edu.au/].
• [19] X. B. Zhang, J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its applications, Comput. Math. Appl. 61 (2011), 722–730.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.