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In this paper, we shall show that for any entire function f,
the function of the form f^m(f^n^(−1))f' has no non-zero finite Picard
value for all positive integers m, n ∈ N possibly except for the special
case m = n = 1. Furthermore, we shall also show that for any two nonconstant
meromorphic functions f and g, if f^m(f^n(−1))f' and g^m(g^(n−1))g'
share the value 1 weakly, then f ≡ g provided that m and n satisfy some
conditions. In particular, if f and g are entire, then the restrictions on
m and n could be greatly reduced.
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참고문헌 (13)
참고문헌 신청
C. C. Yang / 1972 / On deficiencies of differential polynomials. II / Math. Z. 125 : 107 ~ 112
C. C. Yang / 1997 / Unique polynomials of entire and meromorphic functions / Mat. Fiz. Anal. Geom. 4 (3) : 391 ~ 398
C. C. Yang / 1997 / Uniqueness and value-sharing of meromorphic functions / Ann. Acad. Sci. Fenn. Math 22 (2) : 395 ~ 406
C. C. Yang / 2003 / Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications / Kluwer Academic Publishers Group : 557 ~
H. X. Yi / 1995 / Meromorphic functions that share one or two values / Complex Variables Theory Appl 28 (1) : 1 ~ 11
C. C. Yang / 1997 / Unique polynomials of entire and meromorphic functions / Mat. Fiz. Anal. Geom. 4 (3) : 391 ~ 398
C. C. Yang / 1997 / Uniqueness and value-sharing of meromorphic functions / Ann. Acad. Sci. Fenn. Math 22 (2) : 395 ~ 406
C. C. Yang / 2003 / Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications / Kluwer Academic Publishers Group : 557 ~
H. X. Yi / 1995 / Meromorphic functions that share one or two values / Complex Variables Theory Appl 28 (1) : 1 ~ 11
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