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Normalized analytic functions with fixed second coefficient

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Abstract

This paper studies normalized analytic functions f with fixed second coefficient defined on open unit disk for which \({(1+z)^2f(z)}/{z}\) and \({(1+z)f(z)}/{z}\) are functions having positive real part. The radius of strongly starlikeness, the radius of lemniscate starlikeness, the radius of parabolic starlikeness and other starlikeness radii estimates are calculated for these functions. As well relevant connections of computed radii estimates with the existing one are also shown.

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Acknowledgements

The authors are grateful to the referees for their helpful suggestions and insights that helped to improve quality and clarity of this manuscript.

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Author notes

  1. N. K. Jain and S. Kumar are contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, University of Delhi, Guru Tegh Bahadur Road, Delhi, 110 007, India

    Swati Anand

  2. Department of Mathematics, Aryabhatta College, Benito Juarez Road, New Delhi, Delhi, 110021, India

    Naveen Kumar Jain

  3. Department of Applied Science, Bharati Vidyapeeth’s College of Engineering, New Delhi, Delhi, 110063, India

    Sushil Kumar

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  1. Swati Anand
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  2. Naveen Kumar Jain
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  3. Sushil Kumar
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Correspondence to Naveen Kumar Jain.

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Communicated by S. Ponnusamy.

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Anand, S., Jain, N.K. & Kumar, S. Normalized analytic functions with fixed second coefficient. J Anal 31, 1917–1938 (2023). https://doi.org/10.1007/s41478-022-00544-5

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  • DOI: https://doi.org/10.1007/s41478-022-00544-5

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