On the Study of Meromorphic Functions That Shares Small Functions Partially With the Second Order Difference Operator - Ahmed, Touqeer; Shilpa, N.; Somalatha, M. T. (Communications in Mathematics and Applications, 2022)
In this paper, we looked at some problems with the uniqueness of meromorphic functions with a second order difference operator. We looked at them from the point of view of partial sharing. We have obtained two uniqueness results. In the first theorem \(Δ^2 g(z)\) and \(g(z)\) shares \(a_1(z)\), \(a_2(z)\), \(∞\) CM, whereas in the second theorem \(g(z)\) and \(Δ^2 g(z)\) partially share \(a_1(z)\), \(a_2(z)\) CM that generalizes the results due to Banerjee and Maity (Meromorphic function partially shares small functions or values with its linear c-shift operator, Bulletin of the Korean Mathematical Society 58(5) (2021), 1175 – 1192), and Heittokangas et al., Uniqueness of meromorphic functions sharing values with their shifts, Complex Variables and Elliptic Equations 56(1-4) (2011), 81 – 92.