Published on June 2020 | Functions of complex variables

Set shared by an Entire Function with its k-th Derivative Using Normal Families

In this paper, we study a problem of a non-constant entire function f that Shares a set S = {a, b, c} with its k-th derivative f^(k) , where a, b and c are any three distinct Complex numbers. We have found a gap in the statement of the main result of Chang Fang-Zalcman [10], and with the help of their method, we have generalized their result in A more compact form. As an application, we generalize the famous Br¨uck conjecture [9] with the idea of set sharing.