Argument estimates for certain analytic functions. (English) Zbl 1137.30332

Summary: Let \(p(z)\) be analytic in the open unit disk \(\mathbf U\) with \(p(0)=1\) and \(p'(0)=0\). S. S. Miller and P. T. Mocanu [J. Math. Anal. Appl. 276, No. 1, 90–97 (2002; Zbl 1012.30012)] have obtained some interesting subordination theorems for such functions \(p(z)\). The object of the present paper is to discuss some sufficient conditions for the argument of \(p(z)\) to satisfy \(|\text{arg}\,p(z)|<(\pi/2)\rho\) for \(z\in\mathbf U\).


30C80 Maximum principle, Schwarz’s lemma, Lindelöf principle, analogues and generalizations; subordination
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)


Zbl 1012.30012
Full Text: DOI Euclid


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