Uniqueness Result Concerning First Derivative and Difference of a Meromorphic Function andSufficient Condition for Periodicity

Abstract

In the paper, we discuss the uniqueness problem of meromorphic function \(f(z)\) when \(f^{\prime}(z)\) shares \(a\), \(b\) and \(\infty\) CM with \(\Delta_{c}f(z)\), where \(a\) and \(b\) are two distinct finite values. The obtained result improves the recent result of Qi et al. [6] by dropping the condition ‘‘order of growth of \(f\) is not an integer or infinite’’ by ‘‘\(\rho(f)<\infty\)’’. Also in the paper we give an affirmative answer of the question raised by Wei et al. [9].