Related papers: Value sharing by an entire function with its deriv…
In this paper, we employ the theory of normal families in several complex variables to obtain some uniqueness theorems for entire functions. These results extend the related works of Li and Yi [11], and Lu et al. [18] to the setting of…
In this paper, we prove some uniqueness theorems concerning the derivatives of meromorphic functions when they share three sets. The obtained results improve some recent existing results.
We investigate uniqueness problems for an entire function that shares two small functions of finite order with their difference operators. In particular, we give a generalization of a result in $[2]$.
In the paper, we investigate the uniqueness problem of a power of an entire function that share one value partially with it's linear differential polynomial and obtain a result, which improves several previous results in a large scale. Also…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
In this paper, on the basis of a specific question raised in [6], we further continue our investigations on the uniqueness of a meromorphic function with its higher derivatives sharing two sets and answer the question affirmatively.…
We determine all entire functions $f$ such that for nonzero complex values $a\neq b$ the implications $f=a \Rightarrow f' =a$ and $f' =b \Rightarrow f=b$ hold. This solves an open problem in uniqueness theory. In this context we give a…
In the context of several complex variables, we investigate the uniqueness problem for a power of a meromorphic function that shares a value with its $k$-th order directional derivative in $\mathbb{C}^m$. Our results extend previous…
In this paper, we continue to investigate the uniqueness problem when an entire function $f$ and its linear differential polynomial $L(f)$ share two distinct complex values CMW (counting multiplicities in the weak sense) jointly. Also, We…
We extend to several variables an earlier result of ours, according to which an entire function of one variable of sufficiently small exponential type, having all derivatives of even order taking integer values at two points, is a…
In this paper, we study uniqueness problems for entire functions that partially share two values with their higher-order derivatives. The results obtained here both improve and generalize the related results of Li and Yi \cite{LYi}, L\"{u}…
In this paper, we investigate the sharing values problem that entire function $f(z)$ and its first order difference operator $\Delta_{\eta}f(z)$ share two distinct pairs of finite values IM. We prove: Let $f(z)$ be a non-constant entire…
In the existing literature, many researchers consider the uniqueness of the power of a meromorphic function with its derivative counterpart share certain values or small functions. Here we consider the same problem under the aegis of a more…
A simple proof is given of the known fact that an m-times continuously differentiable function on the real line can be approximated along with its derivatives by an entire function and its respective derivatives.
In this paper, we investigate the uniqueness problem of entire functions that share an entire function with their higher-order difference operators. We obtain two results that confirm the conjectures posed by Liu and Laine \cite{LL1} and by…
In this paper, we study the unicity of entire functions concerning their $q-$shifts and $k-$th derivatives and prove: Let $f(z)$ be a transcendental entire function of zero-order, and $g(z)$ define as in (1.1). Let $a(z), b(z)$ be two…
We prove some uniqueness results for the Riemann zeta-function and the Euler gamma-function by virtue of shared values using the value distribution theory.
We prove that the derivative of a non-linear entire function is unbounded on the preimage of an unbounded set.
Value distribution and uniqueness problems of difference operator of an entire function have been investigated in this article. This research shows that a finite ordered entire function $ f $ when sharing a set $ \mathcal{S}=\{\alpha(z),…
We prove that if two additive functions (from a certain class) take large values with roughly the same probability then they must be identical. This is a consequence of a structure theorem making clear the inter-relation between the…