Normal families and shared functions

• Autorzy: Sun C. X.

Identyfikatory

DOI

10.1515/fascmath-2018-0011

• Języki publikacji: EN

Abstrakty

EN

Let k ϵ N, m ϵ N U {0}, and let a(z)( ≡ 0) be a holomorphic function, all zeros of a(z) have multiplicities at most m. Let F be a family of meromorphic functions in D. If for each f ϵ F, the zeros of f have multiplicities at least k + m + 1 and all poles of f are of multiplicity at least m +1, and for f, g ϵ F, ff^(k) - a(z) and gg^(k) - a(z) share 0, then F is normal in D. Some examples are given to show that the conditions are best, and the result removes the condition “m is an even integer” in the result due to Sun [Kragujevac Journal of Math 38(2), 173-282, 2014].

Słowa kluczowe

EN

meromorphic function; normal criterion; Shared function

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2018
• Tom: Nr 60
• Strony: 173--180
• Opis fizyczny: Bibliogr. 9 poz.

Twórcy

autor

Sun C. X.

• School of Mathematics Xuanwei Senior School Xuanwei 655400, Yunnan Province, PR China

Bibliografia

• [1] Chen H.H., Fang M.L., On the value distribution of fnf’, Sci. China Ser. A, 38(1995), 789-798.
• [2] Chang J.M., Normality and quasinormality of zero-free meromorphic functions, (Engl. Ser.), Acta Math. Sin., 28(2012), 707-716.
• [3] Deng B.M., Fang M.L., Liu D., Normal families of zero-free meromorphic functions, J. Aust. Math. Soc., 91(2011), 313-322.
• [4] Lu Q., Gu Y.X., Zeros of differential polynomial ff(k) - a and its normality, Chinese Quart. J. Math., 24(2009), 75-80.
• [5] Meng D.W., Hu P.Ch., Normality criteria of meromorphic functions sharing one value, J. Math. Anal. Appl., 381(2011), 724-731.
• [6] Sun C.X., Normal families of meromorphic functions sharing a holomorphic function, Kragujevac Journal of Mathematics, 38(2)(2014), 273-282.
• [7] Pang X.C., Zalcman L., Normal families and shared values, Bull. London Math. Soc., 32(2000), 325-331.
• [8] Xu J.F., Cao W.S., Some normality criteria of meromorphic functions, J. Inequal. Appl., (2010), art. ID 926302, 10 pp.
• [9] Zeng S.P., Lahiri I., A normality criterion for meromorphic functions having multiple zeros, Annales Polonici Mathematici, 110(3)(2014), 283-294.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).