Ali, Rosihan M.; Khan, M. Hussain; Ravichandran, V.; Subramanian, K. G. A class of multivalent functions with negative coefficients defined by convolution. (English) Zbl 1105.30002 Bull. Korean Math. Soc. 43, No. 1, 179-18 (2006). Summary: For a given \(p\)-valent analytic function \(g\) with positive coefficients in the open unit disk \(\Delta\), we study a class of functions \(f(z)=z^p-\sum^\infty_{n =m}a_nz^n\) \((a_n\geq 0)\) satisfying \[ \frac 1p \text{Re}\left(\frac{z(f*q)'(z)} {(f*g)(z)} \right)\geq\alpha\quad (0\leq\alpha<1;\;z \in\Delta). \] Coefficient inequalities, distortion and covering theorems, as well as closure theorems are determined. The results obtained extend several known results as special cases. Cited in 11 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) PDFBibTeX XMLCite \textit{R. M. Ali} et al., Bull. Korean Math. Soc. 43, No. 1, 179--18 (2006; Zbl 1105.30002) Full Text: DOI