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Successive coefficients for spirallike and related functions

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Abstract

We consider the family of all analytic and univalent functions in the unit disk of the form \(f(z)=z+a_2z^2+a_3z^3+\cdots \). Our objective in this paper is to estimate the difference of the moduli of successive coefficients, that is \(\big ||a_{n+1}|-|a_n|\big |\), for f belonging to the family of \(\gamma \)-spirallike functions of order \(\alpha \). Our particular results include the case of starlike and convex functions of order \(\alpha \) and other related class of functions.

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Acknowledgements

The authors thank the referee for many useful comments. The work of the second author is supported by Mathematical Research Impact Centric Support (MATRICS) of DST, India (MTR/2017/000367).

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Authors and Affiliations

  1. Discipline of Mathematics, Indian Institute of Technology Indore, Simrol, Khandwa Road, Indore, 453 552, India

    Vibhuti Arora & Swadesh Kumar Sahoo

  2. Department of Mathematics, Indian Institute of Technology Madras, Chennai, 600 036, India

    Saminathan Ponnusamy

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  1. Vibhuti Arora
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  2. Saminathan Ponnusamy
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  3. Swadesh Kumar Sahoo
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Correspondence to Swadesh Kumar Sahoo.

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Arora, V., Ponnusamy, S. & Sahoo, S.K. Successive coefficients for spirallike and related functions. RACSAM 113, 2969–2979 (2019). https://doi.org/10.1007/s13398-019-00664-x

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