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.
Published
2015-06-26
How to Cite
Trąbka-Więcław, M. N. J. S. K. (2015). Some Remarks on Close-to-Convex and Strongly Convex Functions. MATHEMATICA SCANDINAVICA, 116(2), 309-319. https://doi.org/10.7146/math.scand.a-21165
Section
Articles