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COEFFICIENT ESTIMATES FOR SOME CLASSES OF FUNCTIONS ASSOCIATED WITH $q$-FUNCTION THEORY

Part of: Classical measure theory Geometric function theory Elementary classical functions

Published online by Cambridge University Press:  06 March 2017

SARITA AGRAWAL
SARITA AGRAWAL*
Affiliation:
Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa Road, Indore 453 552, India email [email protected]
*
✉[email protected]
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Abstract

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For every $q\in (0,1)$, we obtain the Herglotz representation theorem and discuss the Bieberbach problem for the class of $q$-convex functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$. In addition, we consider the Fekete–Szegö problem and the Hankel determinant problem for the class of $q$-starlike functions, leading to two conjectures for the class of $q$-starlike functions of order $\unicode[STIX]{x1D6FC}$ with $0\leq \unicode[STIX]{x1D6FC}<1$.

Keywords

q-starlike function of order 𝛼q-convex functionHerglotz representationBieberbach’s conjectureFekete–Szegö problemHankel determinant

MSC classification

Primary: 30C50: Coefficient problems for univalent and multivalent functions
Secondary: 28A25: Integration with respect to measures and other set functions 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.) 33B10: Exponential and trigonometric functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 95 , Issue 3 , June 2017 , pp. 446 - 456
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

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