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ON A CLOSE-TO-CONVEX ANALOGUE OF CERTAIN STARLIKE FUNCTIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  22 January 2020

VASUDEVARAO ALLU ,
JANUSZ SOKÓŁ  and
DEREK K. THOMAS
VASUDEVARAO ALLU*
Affiliation:
School of Basic Sciences, Indian Institute of Technology Bhubaneswar, Argul, Bhubaneswar, PIN-752050, Odisha, India email avrao@iitbbs.ac.in
JANUSZ SOKÓŁ
Affiliation:
Faculty of Mathematics and Natural Sciences, University of Rzeszów, ul. Prof. Pigonia 1, 35-310Rzeszów, Poland email jsokol@ur.edu.pl
DEREK K. THOMAS
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, SwanseaSA2 8PP, UK email d.k.thomas@swansea.ac.uk
*
✉avrao@iitbbs.ac.in
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Abstract

For $f$ analytic in the unit disk $\mathbb{D}$, we consider the close-to-convex analogue of a class of starlike functions introduced by R. Singh [‘On a class of star-like functions’, Compos. Math.19(1) (1968), 78–82]. This class of functions is defined by $|zf^{\prime }(z)/g(z)-1|<1$ for $z\in \mathbb{D}$, where $g$ is starlike in $\mathbb{D}$. Coefficient and other results are obtained for this class of functions.

Keywords

univalent functionstarlike functionconvex functionalpha-convex functioncoefficient estimateintegral mean

MSC classification

Primary: 30C50: Coefficient problems for univalent and multivalent functions
Secondary: 30C55: General theory of univalent and multivalent functions 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 102 , Issue 2 , October 2020 , pp. 268 - 281
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Copyright
© 2020 Australian Mathematical Publishing Association Inc.

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