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

Authors

  • Megha M. Manakame Jnanabharathi Campus, Bangalore University, Bangalore. 560056
  • Harina P Waghamore Jnanabharathi Campus, Bangalore University, Bangalore. 560056

DOI:

https://doi.org/10.23755/rm.v48i0.1206

Keywords:

Meromorphic functions, Linear Difference polynomial, Weighted sharing, Uniqueness.

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.

Author Biographies

  • Megha M. Manakame, Jnanabharathi Campus, Bangalore University, Bangalore. 560056

    Department of Mathematics

    Bangalore University

  • Harina P Waghamore, Jnanabharathi Campus, Bangalore University, Bangalore. 560056

    Department of Mathematics

    Bangalore University

References

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Published

2023-12-30

Issue

Vol. 48 (2023)

Section

Volume 48-2023

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