Derivatives of Meromorphic Functions with Multiple Zeros and Small Functions
نویسندگان
چکیده
منابع مشابه
Non-real Zeros of Derivatives of Real Meromorphic Functions
The main result of the paper determines all real meromorphic functions f of finite order in the plane such that f ′ has finitely many zeros while f and f(k), for some k ≥ 2, have finitely many non-real zeros. MSC 2000: 30D20, 30D35.
متن کاملZeros of differences of meromorphic functions
Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = ∆f(z) = f(z+1)− f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f . The results may be viewed as discrete analogues of existing theorems on the zeros of f ′ and f ′/f . MSC 2000: 30D35.
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The paper concerns interesting problems related to the field of Complex Analysis, in particular, Nevanlinna theory of meromorphic functions. We have studied certain uniqueness problem on differential polynomials of meromorphic functions sharing a small function. Outside, in this paper, we also consider the uniqueness of $q-$ shift difference - differential polynomials of mero...
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The purpose of this article is to investigate the uniqueness of meromorphic functions sharing five small functions on annuli.
متن کاملSlowly growing meromorphic functions and the zeros of differences
Let f be a function transcendental and meromorphic in the plane with lim inf r→∞ T (r, f) (log r)2 = 0. Let q ∈ C with |q| > 1. It is shown that at least one of the functions F (z) = f(qz)− f(z), G(z) = F (z) f(z) has infinitely many zeros. This result is sharp. MSC 2000: 30D35.
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ژورنال
عنوان ژورنال: Abstract and Applied Analysis
سال: 2014
ISSN: 1085-3375,1687-0409
DOI: 10.1155/2014/310251