El-Ashwah, R. M.; Aouf, M. K.; Moustafa, A. O. Starlike and convexity properties for \(p\)-valent hypergeometric functions. (English) Zbl 1212.30041 Acta Math. Univ. Comen., New Ser. 79, No. 1, 55-64 (2010). Summary: Given the hypergeometric function \(F(a,b;c;z)=\sum ^\infty _{n=0} \frac {(a)_n(b)_n}{(c)_n(1)_n}z^n\), we place conditions on \(a\), \(b\) and \(c\) to guarante that \(z^pF(a, b; c; z)\) will be in various subclasses of \(p\)-valent starlike and \(p\)-valent convex functions. Operators related to the hypergeometric function are also examined. Cited in 2 Documents MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:\(p\)-valent; starlike; convex; hypergeometric function PDFBibTeX XMLCite \textit{R. M. El-Ashwah} et al., Acta Math. Univ. Comen., New Ser. 79, No. 1, 55--64 (2010; Zbl 1212.30041) Full Text: EuDML