[PDF] Top 20 The zeros of differential difference polynomials of certain types

... part in considering the difference analogues of Nevanlinna theory. With the development of difference analogue of Nevanlinna theory, many authors paid their attention to the zero distribution of difference ... See full document

... the zeros of differential polynomials has always been an important research problem in value distribution of meromorphic ...the zeros of difference ... See full document

... the zeros distribution of f (z)P(z, f ) – q(z), where P(z,f ) is a linear differential-difference polynomial of a finite-order transcendental entire function f (z), and q(z) is a nonzero ...a certain extent, ... See full document

... Let f and g be two non-constant meromorphic functions in the complex plane. By S(r, f ), we denote any quantity satisfying S(r, f ) = o(T (r, f )) as r → ∞, possibly outside a set of r with finite linear measure. Then the ... See full document

... A meromorphic function α(z) is called a small function with respect to f (z), if T(r, α) = S(r, f ), where S(r, f ) denotes any quantity satisfying S(r, f ) = o(T (r, f )) as r → ∞ outside a possible exceptional set E of ... See full document

... 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

... m(r , f ) ≤ N r , Q ∗ [f ] − N r , 0; Q ∗ [f ] + S(r , f ). (3.8) From (3.5) we see that possible poles of Q ∗ [f ] occur at the poles of f and zeros of F and P [f ]. Also we note that the zeros of F and P ... See full document

... 3. Beardon, AF: Entire solutions of f(kz) = kf (z)f (z). Comput. Methods Funct. Theory 12(1), 273-278 (2012) 4. Goldstein, R: Some results on factorization of meromorphic functions. J. Lond. Math. Soc. 4(2), 357-364 ... See full document

... In studying differential equations in the complex plane C, it is always an interesting and quite difficult problem to prove the existence or uniqueness of the entire or meromorphic solution of a given equation. There have ... See full document

... possibly outside of a set E with finite linear measure, not necessarily the same at each occurrence. A meromorphic function a(z) is said to be a small function with respect to f (z) if T (r, a) = S(r, f ). We say that two ... See full document

... Picard exceptional value, a transcendental meromorphic functions has at most two picard exceptional values. The classical problem of value distributions of differential polynomials is Hayman conjecture ... See full document

... Rigorous mathematical proofs of the Anderson localization were given by Goldsheid- Molchanov-Pastur [GMP] for one-dimensional models and by Fr¨ohlich-Spencer [FS] for multidimensional Schr¨odinger operators. We should ... See full document

... A large number of research papers have been published so far on the location in the complex plane of some or all of the zeros of a polynomial in terms of the coefficients of the polyno[r] ... See full document

... Gulzar, On the Zeros of Complex Polynomials in a Given Circle, International Journal of Engineering Research and Development, Vol. Marden, Geometry of Polynomials,Math[r] ... See full document

... of zeros of a polynomial in a given circle is of great interest in the theory of the distribution of zeros of ...under certain conditions on the coefficients of the polynomial or their real and ... See full document

... The zeros of this equation are well documented and since many research papers have been interested in the stability of the solution of the differential-difference equation[r] ... See full document

... depends on the estimate of the cardinality of the following set { where and are the partial derivative of with respect to and . In this paper, we discuss the cardinality, of the set of solutions for congruence equations ... See full document

... In this paper, we obtain some generalizations of a well-known result of Enestr¨ om-Kakeya concerning the bounds for the moduli of the zeros of polynomials which extend certain known resu[r] ... See full document

... Let f be a function transcendental and meromorphic in the plane. The forward differ- ence is defined in the standard way by f (z) = f (z + ) – f (z). In what follows, we assume the reader is familiar with the basic ... See full document

... Takedown If you consider content in White Rose Research Online to be in breach of UK law, please notify us by emailing [email protected] including the URL of the record and the rea[r] ... See full document