On a subclass of analytic functions based on Salagean operator (Q2782473)

By using the Sălăgean differential operator \(D^n(n\in\mathbb{N}= \{1,2,\dots\})\) the authors introduce in this paper a class \(R_n(\alpha, \beta, \gamma)\) of analytic and univalent functions \(f(z)\) of the form NEWLINE\[NEWLINEf(z)=z-\sum^\infty_{k=2} a_kz^k,\;e^{i\lambda} a_k\leq 0,\;|\gamma |< \pi/2NEWLINE\]NEWLINE and \(|z|>1\) satisfying NEWLINE\[NEWLINE\text{Re} \biggl\{\bigl((1-\alpha)\bigl( D^nf(z) \bigr)'+ \alpha\bigl(D^{n+1} f(z) \bigr)'\biggr) e^{i\gamma} \biggr\}> \betaNEWLINE\]NEWLINE \(0\leq\beta <\cos\gamma\) and some \(\alpha\leq 1)\). Coefficient estimates, distortion inequalities and radii of starlikeness and conexity for functions in this class are obtained. Modified Hadamard product of functions in this class is also discussed.NEWLINENEWLINEFor the entire collection see [Zbl 0980.00021].