Meromorphic function sharing three sets with its shift, q-shift, q-difference and analogous operators

Author
A. Banerjee1, S. Bhattacharyya2
1) Department of Mathematics, University of Kalyani West Bengal, India; 2) Department of Mathematics, University of Kalyani West Bengal, India
Abstract
Using the notion of weighted sharing of three sets we deal with the uniqueness problem of meromorphic function with its shift, q-shift, q-difference and analogous operator. A handful number of examples have been provided to substantiate our certain claims. In other words, we deduce conditions providing a) $f(z) \equiv t f(z+c)$, where $t^n=1$, $n\ge 2$; b) $f(z)\equiv t f(qz+c)$, where $t^n=1$, $n\ge 2$ and $q , c \in \mathbb{C} \setminus \{0\}$; c) $f(z)\equiv tf(qz)$, where $t^n=1$ and $\mid q \mid =1$; d) $f(z)\equiv \chi_{_n}\Delta_qf$ for $n\ge 2$ with $\Delta_qf=f(qz)-f(z)$ and $\chi_{_n}= \begin{cases} 1, & \mbox{if } n=2, \\ t, & \mbox{if } n \geq 3,\; t^n=1. \end{cases}$
Keywords
meromorphic functions; uniqueness; shift; difference operator; shared set
DOI
doi:10.30970/ms.52.1.38-47
Reference
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Pages
38-47
Volume
52
Issue
1
Year
2019
Journal
Matematychni Studii
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