Results on escaping set of an entire function and its composition

Given two permutable entire functions $f$ and $g,$ we establish vital relationship between escaping sets of entire functions $f,g$ and their composition. We provide some families of transcendental entire functions for which Eremenko’s conjecture holds. In addition, we investigate the dynamical properties of the mapping $f(z)=z+1+e^{-z}\mathrm{.}$