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Applications of Miller-Mocanu’s lemma on certain subclasses of analytic functions. (English) Zbl 1265.30041

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.

MSC:

30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)

Citations:

Zbl 0622.30020
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