On some differential sandwich theorems using an extended generalized Sălăgean operator and extended Ruscheweyh operator

Abstract: In this work we define a new operator using the extended generalized Sălăgean operator and extended Ruscheweyh operator. Denote by $DR^{m,n}_{\lambda}$ the Hadamard product of the extended generalized Sălăgean operator $D^{m}_{\lambda}$ and extended Ruscheweyh operator $R^{n}$, given by $DR^{m,n}_{\lambda}$ : $\mathcal{A}_{\zeta}^{*} \rightarrow \mathcal{A}_{\zeta}^{*}, DR_{\lambda}^{m,n} f (z, \zeta) = (D_{\lambda}^{m} * R^{n}) f (z, \zeta)$ and $\mathcal{A}_{n, \zeta}^{*} = \{f \in \mathcal{H}(U \times \overline{U}), f(z, \zeta) = z+a_{n+1} + \ldots, z \in U, \zeta \in \overline{U}\}$ is the class of normalized analytic functions with $\mathcal{A}_{\zeta}^{*} \rightarrow \mathcal{A}_{\zeta}^{*}$. The purpose of this paper is to introduce sufficient conditions for strong differential subordination and strong differential superordination involving the operator $DR_{\lambda}^{m,n}$ and also to obtain sandwich-type results.