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On convex and starlike functions in a sector

Part of: Geometric function theory

Published online by Cambridge University Press:  09 April 2009

M. Nunokawa  and
D. K. Thomas
M. Nunokawa
Affiliation:
Department of Mathematics Faculty of EducationGunna UniversityMaebashi, Gunma 371, Japan
D. K. Thomas
Affiliation:
Department of MathematicsUniversity of WalesSwansea SA2 8PPUK e-mail: d.k.thomas@swansea.ac.uk
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Abstract

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Let f be analytic in D = {z: |z| < 1} with f(0) = f′(0)−1=0. For γ > 0, the largest α (γ) and β(γ) are found such that . The results solve the inclusion problem for convex and starlike functions defined in a sector.

MSC classification

Secondary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 60 , Issue 3 , June 1996 , pp. 363 - 368
Copyright
Copyright © Australian Mathematical Society 1996

References

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