Fixed Points of Meromorphic Functions Concerning Exponential and Linear Difference Polynomials
DOI:
https://doi.org/10.26713/cma.v14i4.2572Keywords:
Meromorphic function, Linear difference polynomials, Exponential polynomials, Fixed pointsAbstract
In this paper, we analyse the correlation between fixed points of finite order transcendental meromorphic functions, exponential polynomials and linear difference polynomials. Let \(\mathbf{P}_{d}(z,f)\) is a difference polynomial in \(f\) and \(\phi(z)=\sum_{j=1}^{k}P_{j}^{*}e^{Q_{j}^{*}}\) is an exponential polynomial in \(z\). We look upon the zeroes as well as growth of \(f^{n}\mathbf{P}_{d}(z,f)+\phi(z)\). Our results will extend the findings of Fang et al.~(Value distribution of meromorphic functions concerning rational functions and differences, Advances in Difference Equations 2020 (2020), Article number: 692) for linear and exponential difference polynomials.
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