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 \(Δ^2 \mathfrak{g(z)}\) and \(\mathfrak{g(z)}\) shares \(\mathfrak{a}_1\mathfrak{(z)}\), \(\mathfrak{a}_2\mathfrak{(z)}\), \(∞\) CM, whereas in the second theorem \(\mathfrak{g(z)}\) and \(Δ^2 \mathfrak{g(z)}\) partially share \(\mathfrak{a}_1\mathfrak{(z)}\), \(\mathfrak{a}_2\mathfrak{(z)}\) 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.