Dynamics of certain family of transcendental entire functions with infinitely many singular values

In this article, the dynamics of functions in the family \(f_{\lambda }(z)=z-\lambda \sin {z}\) $f_{\lambda }(z)=z-\lambda sinz$ has been studied. It is proved that the family has infinitely many singular values for every choice of non-zero \(\lambda\) $\lambda$ . We discuss how the dynamics of a function belonging to the family changes as the parameter changes. Some specific values of the parameter \(\lambda\) $\lambda$ are given for which the function has wandering domains. We show that when \(\lambda \ge 1\) $\lambda \ge 1$ , the family has no invariant Baker domains. It is proved that for some complex parameter values, the Fatou set contains Siegel discs. Finally, we give a comparison of dynamics of the families \(\lambda \sin {z}\) $\lambda sinz$ , \(\lambda e^z\) $\lambda e^z$ and \(z-\lambda \sin {z}\) $z-\lambda sinz$ through a table.