Meromorphic Function
Unicity of Meromorphic Function Sharing One Small Function with Its Derivative
... nonconstant meromorphic functions; a meromorphic function az / ≡ ∞ is called a small functions with respect to f provided that T r, a Sr, f ...small function of f is a field. Let bz be a small ...
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Zeros and fixed points of the linear combination of shifts of a meromorphic function
... In Theorem D, Bergweiler and Langley considered the existence of zeros of first differ- ence operator when the transcendental meromorphic function is of lower order less than one. Chen and Shon [] ...
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On value distribution and uniqueness of meromorphic function with finite logarithmic order concerning its derivative and q shift difference
... of meromorphic functions will be used (see ...a meromorphic function f (z), we use S(r, f ) to denote any quantity satisfying S(r, f ) = o(T (r, f )) for all r outside a possible exceptional set E of ...
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Some inequalities on meromorphic function and its derivative concerning small functions in an angular domain
... a meromorphic function and its derivative in an angular domain concerning multiple values and small functions and obtain some inequalities of meromorphic functions in an angular domain as ...
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Uniqueness of meromorphic solutions sharing values with a meromorphic function to \(w(z + 1)w(z 1) = h(z)w^{m}(z)\)
... given meromorphic function f (z), we use the standard notation of the Nevanlinna theory (see ...a meromorphic function a(z) is a small function of f (z), if T(r, a) = o(T(r, f )) = S(r, ...
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Uniqueness and value distribution for difference operators of meromorphic function
... The difference Nevanlinna theory and its applications to the uniqueness theory have become a subject of great interest [2-4], recently. With these fundamental results, Heit- tokangas et al. considered a ...
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13. A new subclass of Meromorphic Function with Positive Coefficients
... Abstract. In the present investigation, the authors define a new class of meromorphic functions defined in the punctured unit disk Δ ∗ := {𝑧 ∈ ℂ : 0 < ∣𝑧∣ < 1}. Coefficient inequalities, growth and distortion ...
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Transcendental singularities for a meromorphic function with logarithmic derivative of finite lower order
... entire function of lower order less than 1/2, then the inverse function of f = 1 − 1/g has a direct singularity over 1; in this case, A k obviously has lower order less than 1/2, but the cos πλ theorem [9, ...
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On zeros and deficiencies of differences of meromorphic functions
... The following lemma contains a basic property of meromorphic functions of finite order. Lemma . ([]) Let f (z) be a meromorphic function with ρ(f ) < ∞. Then, for given real constants c > ...
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Non real zeros of derivatives of meromorphic functions
... It would clearly be preferable to know whether Theorem 1.5 holds without hypotheses (c) and (d), but the present method does not deliver this, and in particular it seems difficult to exclude the possibility that f has ...
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Growth Properties of Composition of Two Meromorphic Functions
... Now let h(z) be a non constant meromorphic function in the complex plane C . Let us denote the number of roots of the equation h(z) = a in | z | ≤ r, with due count of multiplicity by n(r, a) for any ...
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Fixed points of differences of meromorphic functions
... Theorem A Let f be a transcendental meromorphic function in the plane. Suppose that there exists a ∈ C with δ(a, f ) > 0 and δ(∞, f ) = 1. Then f has infinitely many fixed points. In this paper, we shall ...
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Meromorphic Functions Sharing Three Values
... Let f and g be two non-constant meromorphic func- tions in the complex plane. It is assumed that the reader is familiar with the standard notations of Nevanlinna’s theory such as T r f , , m r f , , N r f ...
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Some Normality Criteria of Meromorphic Functions
... analytic meromorphic functions which have a common property P in a domain D will in general be a normal family if P reduces an analytic meromorphic function in the open complex plane C to a ...
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Subclasses of Meromorphic Functions Associated with Convolution
... of meromorphic functions in the unit disk are introduced by means of convolution with a given fixed meromorphic ...convoluted-derived function in the class to be subordinated to a given normalized ...
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Derivatives of meromorphic functions of finite order
... If f is a meromorphic function of finite lower order in the plane satisfying condition ii of Theorem 1.2, with k = 2, then f ′ has finitely many critical values and so finitely many asym[r] ...
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Convolution Properties of Classes of Analytic and Meromorphic Functions
... of meromorphic functions in the punctured unit disk are introduced by means of convolution with a given fixed meromorphic ...of meromorphic starlike and convex functions and other related subclasses ...
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5. ON MEROMORPHIC FUNCTIONS THAT SHARE A SMALL FUNCTION WITH ITS DERIVATIVES
... A meromorphic function a is said to be a small function of f where T (r, a) = S(r, f ), that is T (r, a) = o(T (r, f )) as r → ∞, outside of a possible exceptional set of finite linear ...small ...
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Uniqueness of Transcendental Meromorphic Functions with Their Nonlinear Differential Polynomials Sharing the Small Function
... nonconstant meromorphic function f (z) on the complex plane C, we denote by S(r, f ) any quantity satisfying S(r, f ) = o(T(r, f )) as r → ∞ except possibly for a set of r of finite linear ...A ...
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Results on the growth of meromorphic solutions of some linear difference equations with meromorphic coefficients
... a meromorphic function always means meromorphic in the whole complex plane C, and c always means a nonzero ...of meromorphic functions such as T(r, f ), m(r, f ) and N(r, f ) as explained in ...
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