Normal families and shared function II

• Autorzy: Chengxiong Sun
• Języki publikacji: EN

Abstrakty

EN

Let k, n ∈ N,l ∈ N\ {1} , m ∈ N U {0}, and a(z)(≠ 0) be a holomorphic function, all of whose zeros have multiplicities at most m. Let F be a family of meromorphic functions in D such that multiplicities of zeros of each f ∈ F are at least k + m. If for f, g ∈ F satisfy f^l(f^(k))ⁿ and g^l(g^(k))ⁿ share a(z), then F is normal in D. The examples are provided to show that the result is sharp. The result extends the related theorems [9,10,12]. we also omit the conditions “m is divisible by n +1” and “all poles of f have multiplicities at least m + 1” in the result due to Meng, Liu and Xu [12] [Journal of Computational Analysis and Applications 27(3)(2019), 511-526].

Słowa kluczowe

EN

meromorphic function; normal families; shared function

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2019
• Tom: nr 62
• Strony: 141--154
• Opis fizyczny: Bibliogr. 17 poz.

Twórcy

autor

Chengxiong Sun

• Xuanwei No. 9 Senior High School Yunnan, People’s Republic of China

Bibliografia

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• [11] Ding J.J., Ding L.W., Yuan W.J., Normal families of meromorphic functions concerning shared values, Complex Var. Elliptic Equ., 58(1)(2013), 113-121.
• [12] Meng D.W., Liu S.Y., Xu H.Y., Normal criteria of meromorphic functions concerning holomorphic functions, Journal of Computational Analysis and Applications, 27(3)(2019), 511-524.
• [13] Pang X.C., Zalcman L., Normal families and shared values, Bull. London Math. Soc., 32(2000), 325-331.
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• [17] Yang L., Value Distribution Theory, Springer, Berlin, 1993.

Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).