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Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions

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Abstract

The sharp upper and lower bounds on the Hermitian-Toeplitz determinant of third order are computed for the classes of strongly starlike functions, lemniscate starlike functions and lune starlike functions. Moreover, a non-sharp upper bound on the fourth Hankel determinant for the lemniscate starlike functions is also obtained. Relevant connections of our results with the existing ones are also pointed out.

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Acknowledgements

The authors would like to express their gratitude to the referees for many valuable suggestions regarding a previous version of this paper which indeed improved the paper.

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  1. Department of Mathematics, Ramanujan College, University of Delhi, Kalkaji, New Delhi, 110019, India

    Virendra Kumar

  2. Bharati Vidyapeeth’s College of Engineering, Delhi, 110063, India

    Sushil Kumar

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  1. Virendra Kumar
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Correspondence to Sushil Kumar.

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Kumar, V., Kumar, S. Bounds on Hermitian-Toeplitz and Hankel determinants for strongly starlike functions. Bol. Soc. Mat. Mex. 27, 55 (2021). https://doi.org/10.1007/s40590-021-00362-y

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  • DOI: https://doi.org/10.1007/s40590-021-00362-y

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