Geodesic
Normality through sharing of pairs of functions with derivatives
Filomat, Tome 37 (2023) no. 20, p. 6709

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DOI

Let F ⊂M(D) and let a, b and c be three distinct complex numbers. If, there exist a holomorphic function h on D and a positive constant ρ such that for each f ∈ F , f and f ′ partially share three pairs of functions (a, h), (b, cf ) and (c, df ) on D, where cf and df are some values in some punctured disk D∗ ρ(0), then F is normal in D. This is an improvement of Schwick’s result [Arch. Math. (Basel), 59 (1992), 50-54]. We also obtain several normality criteria which significantly improve the existing results and examples are given to establish the sharpness of results
DOI : 10.2298/FIL2320709C
Classification : 30D30, 30D45
Keywords: Normal family, Shared value, Meromorphic function 
Kuldeep Singh Charak; Manish Kumar; Anil Singh. Normality through sharing of pairs of functions with derivatives. Filomat, Tome 37 (2023) no. 20, p. 6709 . doi: 10.2298/FIL2320709C
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     title = {Normality through sharing of pairs of functions with derivatives},
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     doi = {10.2298/FIL2320709C},
     language = {en},
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