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

• Autores: Katarzyna Trabka-Wieclaw, Mamoru Nunokawa, Janusz Sokól
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 116, Nº 2, 2015, págs. 309-319
• Idioma: inglés
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• Resumen

  • 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.