On a class of meromorphic multivalent functions (Q1887409)

A function \(f(z)= z^{-p}+ \sum^\infty_{m=k-p} a_m z^m\), \(0<|z|< 1,\,p,\,k\)-positive integers, is said to belong to the class \(M(p,k,\alpha,\lambda)\) if it satisfies the condition \[ |(1+ p\alpha)z^p f(z)+\alpha z^{p+1} f'(z)- 1|< \lambda, \] where \(\text{Re}(\alpha)\geq 0\), \(\alpha\neq 0\), \(\lambda> 0\). The author investigated various problems (starlikeness, convolution, partial sums) for functions in \(M(p,k,\alpha,\lambda)\). Proofs are based on a result due to \textit{S. S. Miller} and \textit{P. T. Mocanu} [Mich. Math. J. 28, 157--171 (1981; Zbl 0439.30015)].