### Weighted sharing of meromorphic functions concerning certain type of linear difference polynomials

#### Abstract

In this research article, with the help of Nevanlinna theory we study the uniqueness problems of transcendental meromorphic functions having finite order in the complex plane $\mathbb{C}$, of the form is given by $\phi^{n}(z)\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ and $\psi^{n}(z)\sum_{j=1}^{d}a_{j}\psi(z+c_{j})$ where $L(z,\phi)=\sum_{j=1}^{d}a_{j}\phi(z+c_{j})$ which share a non-zero polynomial $p(z)$ with finite weight. By considering the concept of weighted sharing introduced by I. Lahiri (Complex Variables and Elliptic equations,2001,241-253), we investigate difference polynomials for the cases $(0,2),(0,1),(0,0)$. Our new findings extends and generalizes some classical results of Sujoy Majumder\cite{m11}. Some examples have been exhibited which are relevant to the content of the paper.

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DOI: http://dx.doi.org/10.23755/rm.v48i0.1206

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