A note on the uniqueness of certain types of differential-difference polynomials

UDC 517.9 We study the uniqueness problems of certain types of differential-difference polynomials sharing a small function.In this paper, we not only solve the open problem occurred in [A. Banerjee, S. Majumder, <em>On the uniqueness of certain types of differential-difference polynomials</em>, Anal. Math., <strong>43</strong>, № 3, 415-444 (2017)], but also present our main results in a more generalized way.

Value Distribution and Uniqueness of Certain Higher Order q-difference Polynomials

In this paper, by using Nevanlinna theory we investigate cer- tain types of higher order q-di erence polynomials and prove the results on value distribution and uniqueness.

Results on uniqueness of entire functions related to differential-difference polynomial

In the paper, we use the idea of normal family to investigate the uniqueness problems of entire functions when certain types of differential-difference polynomials generated by them sharing a non-zero polynomial. Also we exhibit one example to show that the conditions of our results are the best possible.

Uniqueness of difference polynomials

<abstract><p>Let $ f(z) $ be a transcendental meromorphic function of finite order and $ c\in\Bbb{C} $ be a nonzero constant. For any $ n\in\Bbb{N}^{+} $, suppose that $ P(z, f) $ is a difference polynomial in $ f(z) $ such as $ P(z, f) = a_{n}f(z+nc)+a_{n-1}f(z+(n-1)c)+\cdots+a_{1}f(z+c)+a_{0}f(z) $, where $ a_{k} (k = 0, 1, 2, \cdots, n) $ are not all zero complex numbers. In this paper, the authors investigate the uniqueness problems of $ P(z, f) $.</p></abstract>