Value distribution of difference and q-difference polynomials

VALUE DISTRIBUTION AND UNIQUENESS OF q-SHIFT DIFFERENCE POLYNOMIALS

In this paper, we deal with the distribution of zeros of q-shift difference polynomials of transcendental entire functions of zero order. At the same time we also investigate the uniqueness problems when two difference products of entire functions share one value with finite weight. The results of the paper improve and generalize some recent results due to Xu, Liu and Cao [Math. Commun. 20 (201...

Some results on value distribution of the difference operator

In this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. Suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $E_k(1, f^{n}(z)f(z+c))=E_k(1, g^{n}(z)g(z+c))$. Then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...

Value Distributions and Uniqueness of Difference Polynomials

Boundary Value Problems for q-Difference Inclusions

and Applied Analysis 3 and for a 0, we denote Iqf x ∫x 0 f t dqt ∞ ∑ n 0 x ( 1 − qqnfxqn, 2.4 provided the series converges. If a ∈ 0, b and f is defined in the interval 0, b , then ∫b a f t dqt ∫b 0 f t dqt − ∫a 0 f t dqt. 2.5 Similarly, we have I0 qf t f t , I n q f t IqI n−1 q f t , n ∈ . 2.6

some results on value distribution of the difference operator

in this article, we consider the uniqueness of the difference monomials $f^{n}(z)f(z+c)$. suppose that $f(z)$ and $g(z)$ are transcendental meromorphic functions with finite order and $e_k(1, f^{n}(z)f(z+c))=e_k(1, g^{n}(z)g(z+c))$. then we prove that if one of the following holds (i) $n geq 14$ and $kgeq 3$, (ii) $n geq 16$ and $k=2$, (iii) $n geq 22$ and $k=1$, then $f(z)equiv t_1g(z)$ or $f(...