arXiv subjects

Jayanta Kamila

Publications and source records attributed to Jayanta Kamila.

3 recordsLinked to original sources

arXiv2021

Some results on the unique range sets

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.

math.CV↗

arXiv2021

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

This paper studies the uniqueness of two non-integral finite ordered meromorphic functions with finitely many poles when they share two finite sets. Also, studies an answer to a question posed by Gross for a particular class of meromorphic functions. Moreover, some observations are made on some results due to Sahoo and Karmakar ( Acta Univ. Sapientiae, Mathematica, DOI: 10.2478/ausm-2018-0025) and Sahoo and Sarkar (Bol. Soc. Mat. Mex., DOI: 10.1007/s40590-019-00260-4).

math.CV↗

arXiv2019

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.

math.CV↗