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Afrika Matematika

, Volume 29, Issue 5–6, pp 793–802 | Cite as

Unpredictability of initial coefficient bounds for m-fold symmetric bi-univalent starlike and convex functions defined by subordinations

  • Murat Çağlar
  • Palpandy Gurusamy
  • Erhan Deniz
Article

Abstract

In this paper, we introduce certain new subclasses of the bi-univalent function class \(\sigma \) in which both f and \(f^{-1}\) are m-fold symmetric analytic with their derivatives in the class \({\mathcal {P}}\) of analytic functions. Furthermore, we obtain coefficient bounds of \(|a_{m+1}|\) and \(|a_{2m+1}|\) for these new subclasses.

Keywords

Analytic functions Univalent functions Bi-univalent functions Taylor–Maclaurin coefficients m-fold symmetric functions Subordination 

Mathematics Subject Classification

Primary 30C45 33C50 Secondary 30C80 

Notes

Acknowledgements

The authors Murat Çağlar and Erhan Deniz were supported by Kafkas University BAP-2016-FM-67 (The Scientific Research Projects Coordination Unit).

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Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2018

Authors and Affiliations

  • Murat Çağlar
    • 1
  • Palpandy Gurusamy
    • 2
  • Erhan Deniz
    • 1
  1. 1.Department of Mathematics, Faculty of Science and LettersKafkas UniversityKarsTurkey
  2. 2.Department of MathematicsVelammal Engineering CollegeChennaiIndia

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