Darus, Maslina; Faisal, Imran; Shareef, Zahid Applications of Miller-Mocanu’s lemma on certain subclasses of analytic functions. (English) Zbl 1265.30041 C. R. Acad. Bulg. Sci. 65, No. 1, 19-24 (2012). The authors define a new type differential operator in the class of \(p\)-valent functions, analytic in the open unit disc \(\mathbb{U} \subset\mathbb{C}\). They use it to study some properties related to subordination and superordination for functions analytic in \(\mathbb{U}\). The proof of the main result (Theorem 3.1) relies heavily on a lemma shown by S. S. Miller and P. T. Mocanu in [Proc. Am. Math. Soc. 99, 527–534 (1987; Zbl 0622.30020)]. At the end of the paper several sufficient conditions for strongly starlike and strongly convex functions are given. Reviewer: Petar Popivanov (Sofia) MSC: 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) Keywords:analytic function; \(p\)-valent function; differential operator; subordination; superordination Citations:Zbl 0622.30020 PDFBibTeX XMLCite \textit{M. Darus} et al., C. R. Acad. Bulg. Sci. 65, No. 1, 19--24 (2012; Zbl 1265.30041)