[PDF] Top 20 Value distribution of difference and q difference polynomials

... Recently, a number of papers concerning the complex difference products and the differ- ences analogues of Nevanlinna’s theory have been published (see [–] for example), and many excellent results have been obtained. In ... See full document

... studying difference equations in the complex ...on difference operator. Bergweiler and Langley [ 12] considered the value distribution of zeros of difference operators that can be ... See full document

... Remark 1.1. Theorem A implies that the Picard exception value of fz n fz c cannot be nonzero constant. However, Theorem A does not remain valid for meromorphic functions. For example, f z e z − 1/e z 1, n 2, 3, c ... See full document

... 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 ... See full document

... 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 ... See full document

... Let f (z) and g(z) be two 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) coincide ... See full document

... Recently, the difference variant of the Nevanlinna theory has been established indepen- dently in [–]. Using these theories, value distributions of difference polynomials have been studied by many papers. ... See full document

... complex q-difference ...and value distribution of meromorphic solutions of differential ...linear q-difference equations, Barnett et ...the q-difference analog of the lemma on the logarith- ... See full document

... to difference operators. This has lead to development of difference counterparts of many central results of Nevanlinna theory as more efficient tools to study difference ...this difference ... See full document

... δ(a, Q(z, f )) < . Therefore, Q(z, f ) takes every nonzero finite value infinitely ...deficient value plays an important role in the theory of value distribution of meromorphic ... See full document

... non-zero value infinitely ...non-zero value infinitely ...differential polynomials has always been an important research problem in value distribution of meromorphic ...ros ... See full document

... and q-differences in the complex plane C , and a number of papers (including [–]) have focused on the value distribution and uniqueness of differences and differences operator analogs of Nevanlinna ... See full document

... In this paper, we shall assume that the reader is familiar with the fundamental results and the standard notation of the Nevanlinna value distribution theory of meromorphic func- tions (see [, ]). The ... See full document

... specific q-shift difference polynomials of meromorphic functions by Nevanlinna and value distribution theory and extend previous ...of value distribution on q-shift ... See full document

... The quantum calculus is known as the calculus without limits and provides a descent approach to deal with sets of nondifferentiable functions by considering difference opera- tors. Quantum difference operators play an ... See full document

... Strip conditions appear in the mathematical modeling of certain real world problems. For motivation, discussion on multi-strip boundary conditions, examples and a consistent bibliography on these problems, we refer to ... See full document

... A meromorphic (respectively entire) function always means a non-constant function meromorphic (respectively analytic) in the complex plane. Nevanlinna theory of value distribution is concerned with the ... See full document

... of q-difference equations has evolved into a multidisciplinary subject in the last few ...orthogonal polynomials and Bessel functions [1,2]. For some pioneer work on q-difference ... See full document

... for solving the nonlocal boundary value problem of nonlinear nth-order q-difference equations. The numerical experiments show that the algorithm is quite accurate and efficient. Moreover, numerical results are ... See full document

... In this work, we study a boundary value problem for a fractional q-difference equation. By using the monotone iterative technique and lower-upper solution method, we get the existence of positive or negative ... See full document