Related papers: Entire functions with separated zeros and $1$-poin…

We prove that entire transcendental holomorphic functions with an omitted value have infinite entropy. A proof for general transcendental entire functions will be given in an upcoming paper.

We study entire functions whose zeros and one-points lie on distinct finite systems of rays. General restrictions on these rays are obtained. Non-trivial examples of entire functions with zeros and one-points on different rays are…

A transcendental function usually returns transcendental values at algebraic points. The (algebraic) exceptions form the so-called \emph{exceptional set}, as for instance the unitary set $\{0\}$ for the function $f(z) = e^z \,$, according…

We give an example of a convex, finite and lower semicontinuous function whose subdifferential is everywhere empty. This is possible since the function is defined on an incomplete normed space. The function serves as a universal…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. The construction involves an iteration procedure on an infinite-dimensional…

Let f be a function transcendental and meromorphic in the plane, and define g(z) by g(z) = f(z+1) - f(z). A number of results are proved concerning the existence of zeros of g(z) or g(z)/f(z), in terms of the growth and the poles of f.

Let f be a transcendental entire function that omits a complex value a. We show that for every simply connected region D that does not contain a the full preimage of D is disconnected. We conjecture that the same holds if one only assumes…

Baker's conjecture states that a transcendental entire function of order less than $1/2$ has no unbounded Fatou components. It is known that, for such functions, there are no unbounded periodic Fatou components and so it remains to show…

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 $[2]$.

We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…

For a transcendental entire function, a partial affirmative answer to Baker's question on the boundedness of its Fatou components is given. In addition, we have addressed Wang's question on Fej\'er gaps. Certain results about functions with…

We classify transcendental entire functions that are compositions of a polynomial and the exponential for which all singular values escape on disjoint rays. We focus on the case where the escape is degenerate in the sense that points from…

We show that there exist unbounded functionals on the spaces of sequences that take at most one nonzero value on an arbitrary family of elements whose supports are pairwise disjoint.

A general class of transcendental equations in complex domain is considered for functions belonging to the Stieltjes cone. Under certain conditions each transcendental equation has no solution or one, at most, in the complex plane cut along…

In this paper, we study about existence and non-existence of finite order transcendental entire solutions of the certain non-linear differential-difference equations. We also study about conjectures posed by Rong et al. and Chen et al.

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…

For a second order linear differential equation $f''+A(z)f'+B(z)f=0$, with $ A(z)$ and $B(z)$ being transcendental entire functions under some restriction, we have established that all non-trivial solutions are of infinite order. In…

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].

The uniqueness problems on transcendental meromorphic or entire functions sharing at least two values with their derivatives or linear differential polynomials have been studied and many results have been obtained. In this paper, we study a…

We announce conditions under which a given sequence of points on the complex plane is a subsequence of zeros of an entire function with weight restrictions on growth.