Uniqueness theorems of meromorphic functions of a certain form
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
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.
Abstract
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.
참고문헌 (13)
- J. Clunie, "On integral and meromorphic functions", J. London Math. Soc, 37, pp.17~27 (1962)
- J. Clunie, "On a result of Hayman", J. London Math. Soc, 42, pp.389~392 (1967)
- M. L. Fang, "A unicity theorem for entire functions concerning differential polynomials", Indian J. Pure Appl. Math, 32(9), pp.1343~1348 (2001)
- W. K. Hayman, "Meromorphic Functions" (1964), Clarendon Press
- W. K. Hayman, "Research Problems in Function Theory" (1967), The Athlone Press University of London
- W. K. Hayman, "Picard values of meromorphic functions and their derivatives", Ann. of Math, 70, pp.9~42 (1959)
- P. C. Hu, "Unicity of Meromorphic Mappings, Advances in Complex Analysis and its Applications", pp.1~ (2003), Kluwer Academic Publishers
- W. C. Lin, "Uniqueness theorems for meromorphic function", Indian J. Pure Appl. Math, 35(2), pp.121~132 (2004)
- C. C. Yang, "On deficiencies of differential polynomials. II", Math. Z., 125, pp.107~112 (1972)
- C. C. Yang, "Uniqueness and value-sharing of meromorphic functions", Ann. Acad. Sci. Fenn. Math, 22(2), pp.395~406 (1997)
- C. C. Yang, "Unique polynomials of entire and meromorphic functions", Mat. Fiz. Anal. Geom., 4(3), pp.391~398 (1997)
- C. C. Yang, "Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications", pp.557~ (2003), Kluwer Academic Publishers Group
- H. X. Yi, "Meromorphic functions that share one or two values", Complex Variables Theory Appl, 28(1), pp.1~11 (1995)