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Some Remarks on Close-to-Convex and Strongly Convex Functions

Mamoru Nunokawa, Janusz Sokół, Katarzyna Trąbka-Więcław

Abstract


We consider questions of the following kind: When does boundedness of $|{\arg \{1+zp'(z)/p(z)\}}|$, for a given analytic function $p$, imply boundedness of $|{\arg\{p(z)\}}|$? The paper determines the order of strong close-to-convexity in the class of strongly convex functions. Also, we consider conditions that are sufficient for a function to be a Bazilevič function.

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DOI: http://dx.doi.org/10.7146/math.scand.a-21165

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ISSN 0025-5521 (print) ISSN 1903-1807 (online)

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