[PDF] Top 20 The zeros of q shift difference polynomials of meromorphic functions
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The zeros of q shift difference polynomials of meromorphic functions
... It is clear that the logarithmic order of a non-constant rational function is , but there exist infinitely many transcendental entire functions of logarithmic order from Theo- rem . []. Hence, the ... See full document
10
Non real zeros of derivatives of meromorphic functions
... The last assertion is proved as in [38, Lemma 11]. Since f 00 /f 0 has finitely many zeros, the same result of Lewis, Rossi and Weitsman [41] as used in Lemma 7.7 gives a path γ tending to infinity on which f 0 ... See full document
38
On zeros and deficiencies of differences of meromorphic functions
... In this paper, we assume that the reader is familiar with the standard notations of Nevan- linna theory of meromorphic functions (see [, ] or []). In particular, for a meromor- phic function f (z) in the ... See full document
10
Zeros of some difference polynomials
... δ(a, Q(z, f )) < . Therefore, Q(z, f ) takes every nonzero finite value infinitely ...of meromorphic functions. In this paper, we consider the meromorphic function f (z) having ... See full document
11
The zeros of complex differential difference polynomials
... transcendental meromorphic function, then f n f takes every finite non-zero value infinitely ...transcendental meromorphic function and n ≥ , then f n f takes every finite non-zero value infinitely ...the ... See full document
11
Uniqueness of Meromorphic Functions and Differential Polynomials
... at zeros of f k1 and g k1 and poles of f and g, and those 1-points of f k and g k whose multiplicities are distinct from the multiplicities of correspond to 1-points of g k and f k , ... See full document
13
Zeros and value sharing results for q-shifts difference and differential polynomials
... transcendental meromorphic functions has at most two picard exceptional ...differential polynomials is Hayman conjecture ...transcendental meromorphic function and n ∈ N, then f n f 0 takes ... See full document
11
Notes on the uniqueness of meromorphic functions concerning differential polynomials
... We assume that the reader is familiar with the usual notation and basic results of the Nevanlinna theory [4, 10]. Let f (z) and g(z) be two nonconstant meromorphic functions, and let a be a complex number. ... See full document
14
Normality of meromorphic functions and differential polynomials share values
... ) = , for any j ∈ N. This implies that the family F fails to be equicontinuous at , and thus F is not normal at . Remark . This example shows that h(z) – to have at least two distinct zeros (h(z) – b to ... See full document
9
Unicity of meromorphic functions and their linear differential polynomials
... Let a, f , g be some meromorphic functions on C. a is said to be a small function to f , provided T (r, a) = S(r, f ). Given a, a small function to both f and g or some value in C ∪ {∞}, one says that f and ... See full document
6
Uniqueness of difference operators of meromorphic functions
... two meromorphic functions, and let a(z) be a small function with respect to f(z) and ...same zeros (ignoring multiplicities), and we say that f(z) and g (z) share a(z) CM, provided that f(z) - a(z) ... See full document
9
The zeros on complex differential difference polynomials of certain types
... Some researchers improved Theorem B in different ways; for example, the constant a was replaced by a nonzero polynomial in [13]. In addition, the papers [12, 16, 19] are de- voted to the cases of meromorphic ... See full document
14
Growth properties at infinity for solutions of modified Laplace equations
... Wang, YF, Fang, ML: Picard values and normal families of meromorphic functions with multiple zeros.. Schiff, J: Normal Families.[r] ... See full document
7
Meromorphic functions that share a polynomial with their difference operators
... Definition 6 Let f and g be two meromorphic functions, and p be a polynomial. We say that f and g share p CM, provided that f (z) – p(z) and g(z) – p(z) have the same zeros counting multiplicity. And ... See full document
15
Properties of q shift difference differential polynomials of meromorphic functions
... the zeros of f (z) – a and g(z) – a (if a = ∞, zeros of f (z) – a and g(z) – a are the poles of f (z) and g(z), respectively) coincide in locations and multiplicities we say that f (z) and g(z) share the ... See full document
16
Some Uniqueness Results of Q Shift Difference Polynomials Involving Sharing Functions
... specific q-shift difference polynomials of meromorphic functions by Nevanlinna and value distribution theory and extend previous ...on q-shift difference ... See full document
11
On the value distribution and uniqueness of difference polynomials of meromorphic functions
... nonconstant meromorphic functions for some a ∈ C ∪ {∞}. If the zeros of f (z) – a and g(z) – a (if a = ∞ , zeros of f (z) – a and g(z) – a are the poles of f (z) and g(z) respectively) ... See full document
15
Meromorphic functions sharing small functions with their linear difference polynomials
... two meromorphic functions f (z) and g(z), and a ∈ S(f ) ∪ S(g) ∪ {∞} , we say that f (z) and g(z) share a CM when f (z) – a and g(z) – a have the same zeros counting ...a shift of f ... See full document
6
Analog of Hayman Conjecture for Linear Dierence Polynomials
... of Meromorphic functions is an important part of Nevan- linna ...of meromorphic functions sharing values with their shifts or difference ... See full document
10
On value distribution and uniqueness of meromorphic function with finite logarithmic order concerning its derivative and q shift difference
... Meantime, q-difference analogies of the Nevanlinna theory and their applications on the value distribution of q-difference polynomials and q-shift-difference equations are also studied ... See full document
11
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