Fixed Points of Meromorphic Functions Concerning Exponential and Linear Difference Polynomials - Pattar, Jayashri; Shilpa, N. (Communications in Mathematics and Applications, 2023)
In this paper, we analyse the correlation between fixed points of finite order transcendental meromorphic functions, exponential polynomials and linear difference polynomials. Let \(P_{d}(z,f)\) is a difference polynomial in \(f\) and \(φ(z)=\sum_{j=1}^{k}P_{j}^{*}e^{Q_{j}^{*}}\) is an exponential polynomial in \(z\). We look upon the zeroes as well as growth of \(f^{n}P_{d}(z,f)+φ(z)\). 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.
Keywords: Meromorphic function; Linear difference polynomials; Exponential polynomials; Fixed points