# tailieunhanh - Uniqueness of derivatives of meromorphic functions sharing two or three sets

## In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained five results which will improve all the existing results. | Turk J Math 34 (2010) , 21 – 34. ¨ ITAK ˙ c TUB doi: Uniqueness of derivatives of meromorphic functions sharing two or three sets Abhijit Banerjee and Pranab Bhattacharjee Abstract In the paper we consider the problem of uniqueness of derivatives of meromorphic functions when they share two or three sets and obtained ﬁve results which will improve all the existing results. Key word and phrases: Meromorphic functions, uniqueness, weighted sharing, derivative, shared set. 1. Introduction, deﬁnitions and results In this paper by meromorphic functions we will always mean meromorphic functions in the complex plane. It will be convenient to let E denote any set of positive real numbers of ﬁnite linear measure, not necessarily the same at each occurrence. For any non-constant meromorphic function h(z) we denote by S(r, h) any quantity satisfying S(r, h) = o(T (r, h)) (r −→ ∞, r ∈ E). Let f and g be two non-constant meromorphic functions and let a be a ﬁnite complex number. We say that f and g share a CM, provided that f − a and g − a have the same zeros with the same multiplicities. Similarly, we say that f and g share a IM, provided that f − a and g − a have the same zeros ignoring multiplicities. In addition, we say that f and g share ∞ CM, if 1/f and 1/g share 0 CM, and we say that f and g share ∞ IM, if 1/f and 1/g share 0 IM. We denote by T (r) the maximum of T r, f (k) and T r, g(k) . The notation S(r) denotes any quantity satisfying S(r) = o(T (r)) (r −→ ∞, r ∈ E). Let S be a set of distinct elements of C∪ {∞} and Ef (S) = a∈S {z : f(z)−a = 0} , where each zero is counted according to its multiplicity. If we do not count the multiplicity the set Ef (S) = a∈S {z : f(z) − a = 0} is denoted by E f (S). If Ef (S) = Eg (S) we say that f and g share the set S CM. On the other hand, if E f (S) = E g (S), we say that f and g share the set S IM. F. Gross ﬁrst considered the uniqueness of meromorphic functions that share sets of

TÀI LIỆU LIÊN QUAN
4    29    0
9    14    1
8    31    0
7    21    0
25    23    0
8    26    0
7    25    0
6    36    0
14    8    1
11    11    1
TÀI LIỆU XEM NHIỀU
8    19569    4
3    6533    89
14    5231    255
8    4810    1611
2    3121    26
24    3031    56
9    2910    5
35    2825    139
29    2676    78
8    2539    23
TỪ KHÓA LIÊN QUAN
TÀI LIỆU MỚI ĐĂNG
71    3    1    24-06-2021
26    29    0    24-06-2021
2    22    0    24-06-2021
82    2    1    24-06-2021
56    39    0    24-06-2021
5    21    0    24-06-2021
15    1    1    24-06-2021
92    19    0    24-06-2021
11    31    0    24-06-2021
95    3    1    24-06-2021
TÀI LIỆU HOT
8    4810    1611
112    1129    462
122    1080    309
14    5231    255
20    1921    238
36    1582    216
35    1276    211
21    2280    183
16    2261    181
171    1164    179