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ON OZAKI CLOSE-TO-CONVEX FUNCTIONS

Part of: Geometric function theory

Published online by Cambridge University Press:  20 September 2018

VASUDEVARAO ALLU Open the ORCID record for VASUDEVARAO ALLU [Opens in a new window] ,
DEREK K. THOMAS Open the ORCID record for DEREK K. THOMAS [Opens in a new window]  and
NIKOLA TUNESKI Open the ORCID record for NIKOLA TUNESKI [Opens in a new window]
VASUDEVARAO ALLU*
Affiliation:
NFA-18, IIT Campus, Indian Institute of Technology Kharagpur, Kharagpur-721 302, West Bengal, India email alluvasudevarao@gmail.com
DEREK K. THOMAS
Affiliation:
Department of Mathematics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK email d.k.thomas@swansea.ac.uk
NIKOLA TUNESKI
Affiliation:
Faculty of Mechanical Engineering, Ss. Cyril and Methodius University in Skopje, Karpos 2 bb, 1000 Skopje, Republic of Macedonia email nikola.tuneski@mf.edu.mk
*
✉alluvasudevarao@gmail.com
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Abstract

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Let $f$ be analytic in $\mathbb{D}=\{z\in \mathbb{C}:|z|<1\}$ and given by $f(z)=z+\sum _{n=2}^{\infty }a_{n}z^{n}$. We give sharp bounds for the initial coefficients of the Taylor expansion of such functions in the class of strongly Ozaki close-to-convex functions, and of the initial coefficients of the inverse function, together with some growth estimates.

Keywords

analyticunivalentstrongly close-to-convex functionscoefficient estimates

MSC classification

Primary: 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)
Secondary: 30C55: General theory of univalent and multivalent functions
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 1 , February 2019 , pp. 89 - 100
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

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