Functions of One Complex Variable

Let f be a transcendental meromorphic function,a a nonzero finite complex number,and n 2 a positive integer.Then f + a(f')n assumes every complex value infinitely often.This answers a question of Ye for n = 2.A related normality criterion is also given.

On the value distribution of f + a(f')~n

We deal with the uniqueness problems on the meromorphic functions sharing the finite sets.The conclusion improves the results obtained by Yi Hongxun and Zhou Houqing respectively.

On an uniqueness of meromorphic functions sharing two finite sets

In this paper, we prove one value distribution result which leads to some normality criteria for a family of analytic functions.

A Note on the value distribution of a differential monomial and some normality criteria

This paper studies the uniqueness of two non-constant meromorphic functions when they share a finite set Moreover, we will give the existence of unique range sets for meromorphic functions that are zero sets of polynomials that do not necessarily satisfy the Fujimoto's hypothesis

Unique range sets without Fujimoto's hypothesis

This paper studies the uniqueness of two meromorphic functions with finitely many poles and finite non-integral order when they share two finite sets. The motivation for writing this paper is the articles due to Sahoo and Sarkar (Bol. Soc. Mat. Mex., DOI: 10.1007/s40590-019-00260-4) and Chen (Georgian Math. J., DOI. 10.1515/gmj-2019-2073).

Unique range sets of mermorphic functions of non-integer finite order

In this paper, we exhibit the equivalence between different notions of unique range sets, namely, unique range sets, weighted unique range sets and weak-weighted unique range sets under certain conditions.\par Also, we present some uniqueness theorems which show how two meromorphic functions are uniquely determined by their two finite shared sets. Moreover, in the last section, we make some observations that help us to construct other new classes of unique range sets.

Some results on the unique range sets

Let $f$ be a transcendental meromorphic function defined in the complex plane $\\mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(\\geq 2), q_{k}(\\geq 1)$ are $k(\\geq1)$ non-negative integers. We obtain a quantitative estimation of the characteristic function $T(r, f)$ in terms of $\\overline{N}\\left(r,\\frac{1}{f^{q_{_{0}}}(f^{(k)})^{q_{k}}-1}\\right)$.\\par Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., 14, 93-100, 2011) and Karmakar and Sahoo (Results Math., 73, 2018) for a particular class of transcendental meromorphic functions.

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Value distribution of some differential monomials

Let $f$ be a transcendental meromorphic function defined in the complex plane $\mathbb{C}$. We consider the value distribution of the differential polynomial $f^{q_{0}}(f^{(k)})^{q_{k}}$, where $q_{0}(\geq 2), q_{k}(\geq 1)$ are $k(\geq1)$ non-negative integers. We obtain a quantitative estimation of the characteristic function $T(r, f)$ in terms of $\overline{N}\left(r,\frac{1}{f^{q_{_{0}}}(f^{(k)})^{q_{k}}-1}\right)$.\par Our result generalizes the results obtained by Xu et al. (Math. Inequal. Appl., 14, 93-100, 2011) and Karmakar and Sahoo (Results Math., 73, 2018) for a particular class of transcendental meromorphic functions.

Sudip Saha

Papers

Unique range sets of mermorphic functions of non-integer finite order

Some results on the unique range sets

Value distribution of some differential monomials

A Note on the value distribution of a differential monomial and some normality criteria

Value distribution of some differential monomials