Sufficient conditions for analytic functions defined by Frasin differential operator

Abstract

"Very recently, Frasin [7] introduced the differential operator $\mathcal{I}_{m,\lambda }^{\zeta }f(z)$ defined as \begin{equation*} \mathcal{I}_{m,\lambda }^{\zeta }f(z)=z+\sum\limits_{n=2}^{\infty }\left( 1+(n-1)\sum\limits_{j=1}^{m}\binom{m}{j}(-1)^{j+1}\lambda ^{j}\right) ^{\zeta }a_{n}z^{n}. \end{equation*} The current work contributes to give an application of the differential operator $\mathcal{I}_{m,\lambda }^{\zeta }f(z)$ to the differential inequalities in the complex plane."