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

A. Banerjee1, S. Bhattacharyya2
1) Department of Mathematics, University of Kalyani West Bengal, India; 2) Department of Mathematics, University of Kalyani West Bengal, India
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 $\chi_{_n}= \begin{cases} 1, & \mbox{if } n=2, \\ t, & \mbox{if } n \geq 3,\; t^n=1. \end{cases}$
meromorphic functions; uniqueness; shift; difference operator; shared set
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