[PDF] Top 20 Zeros and value sharing results for q-shifts difference and differential polynomials

... 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 density of ... See full document

... exceptional value, a transcendental meromorphic functions has at most two picard exceptional ...of value distributions of differential polynomials is Hayman conjecture ...non-zero value ... 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

... its q-shift f (qz + c) and their derivatives, with small functions of f (z) as the ...fundamental results and the standard notations of the Nevanlinna value distribution theory of meromorphic ... See full document

... the value a IM (ignoring multiplicities) if f (z) – a and g(z) – a have the same ...same zeros with the same multiplicities, then we say that they share the value a CM (counting ...polynomial ... See full document

... fundamental results and the standard notations of the Nevanlinna theory ...finite value a CM when f - a and g - a have the same zeros with the same ... 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 ...recent ... See full document

... [7] Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J. and Zhang, J. (2009) Value Sharing Results for Shifts of Meromorphic Functions, and Sufficient Conditions for Periodicity. Journal of ... 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

... polynomial Q(z, f ) can be called a differential-difference polynomial in f whenever Q(z, f ) is a polynomial in f (z), its shifts f (z + c) and their derivatives, with small functions of f (z) as the ... See full document

... of polynomials have played an important role in many scientific areas such as control theory, signal processing, crytography and mathematical ...the zeros of a polynomial, then the amount of work needed to ... See full document

... of polynomials. 2nd degree and 3rd degree polynomials can be solved very easily, but higher degree complex polynomials of nth degree, n>3, one requires efficient algorithms to find the ...of ... See full document

... the q-poly-tangent polynomials and ...and polynomials, and some integral ...the zeros of the q-poly-tangent polynomials by using a ... See full document

... where the right-hand side is rational in both arguments, has been widely studied during the last decades; see, e.g., [–]. Gundersen et al. [] considered the order of growth of mero- morphic solutions of (.), from ... See full document

... Lemma 2.6 (see [8]) . If P [f ] is as in Lemma 2.4, then T (r , P [f ]) = nT (r , f ) + S(r , f ). 3. The main result. In this section, we present the main result of the paper. Theorem 3.1 . Let f be a transcendental ... See full document

... Mohammad, “On the Zeros of a Certain Class of Polynomials and Related Analytic Functions,” Journal of Mathematical Analysis and Applications, Vol.75, 1980, pp.. Zargar, “Some Extensions [r] ... See full document

... (p, q)-analogue type of Fubini numbers and polynomials and investigate some properties of these ...these polynomials by summation techniques ...(p, q)-Fubini polynomials associated with ... See full document

... Theorem . Let f (z) be a meromorphic function of finite order ρ(f ), let L(z, f ) be a differ- ence polynomial of f (z), and let a, b ∈ S(f ) be two distinct meromorphic functions. Suppose that f (z) and L(z, f ) share ... See full document

... Proof of Theorem 2. By the assumption of the theorems, we know that either both f and g are two transcendental entire functions or both f and g are polynomials. If f and g are transcendental entire functions, ... See full document

... In this paper, we study a nonlinear fractional q-difference equation with nonlocal boundary conditions. The existence of solutions for the problem is shown by applying some well-known tools of fixed-point theory ... See full document