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Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator

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Abstract

Using the Tremblay fractional derivative operator in the complex domain, we introduce and investigate a new class of analytic and bi-univalent functions in the open unit disk. We use the Faber polynomial expansions to obtain upper bounds for the general coefficients of such functions subject to a gap series condition as well as obtaining bounds for their first two coefficients.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada

    H. M. Srivastava

  2. Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, 40402, Taiwan, Republic of China

    H. M. Srivastava

  3. Department of Mathematics, Faculty of Science, Dicle University, 21280, Diyarbakir, Turkey

    S. Sümer Eker

  4. Department of Mathematics, Brigham Young University, Provo, UT, 84602, USA

    S. G. Hamidi

  5. Department of Mathematical Sciences, Kent State University, Burton, OH, 44021-9500, USA

    J. M. Jahangiri

Authors
  1. H. M. Srivastava
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  2. S. Sümer Eker
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  3. S. G. Hamidi
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  4. J. M. Jahangiri
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Corresponding author

Correspondence to S. Sümer Eker.

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Communicated by Ali Abkar.

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Srivastava, H.M., Eker, S.S., Hamidi, S.G. et al. Faber Polynomial Coefficient Estimates for Bi-univalent Functions Defined by the Tremblay Fractional Derivative Operator. Bull. Iran. Math. Soc. 44, 149–157 (2018). https://doi.org/10.1007/s41980-018-0011-3

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  • DOI: https://doi.org/10.1007/s41980-018-0011-3

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