Periodicity of Transcendental Entire Functions Sharing Set with their Shifts

Abstract

This paper aims to study the periodicity of a transcendental entire function of hyper-order less than one. For a transcendental entire function of hyper order less than one and a non-zero complex constant $c$, $\mathfrak{f}(z)\equiv \mathfrak{f}(z+c)$ if they share a certain set with weight two.