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Second Hankel determinant for universally prestarlike functions related with exponential function

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In Ruscheweyh and Salinas (Math Z 263:607–617, 2009) and Ruscheweyh et al. (Isreal J Math 171:285–304, 2009) the researchers introduced universally convex,universally starlike and universally prestarlike functions in the slit domain \( {\mathbb {C}}\backslash [1,\infty {)}.\) These papers extended the corresponding notions from the unit disc to other discs and half-planes containing the origin. In this paper, we consider universally prestarlike generalized functions of order \(\alpha \) with \(\alpha \le 1\) and we obtain upper bounds of the second Hankel determinant \(|a_{2}a_{4}-a_{3}^{2}|\) for such functions related with exponential function.

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References

  1. Ahuja, O.P., Kasthuri, M., Murugusundaramoorthy, G., Vijaya, K.: Upper bounds of second Hankel determinant for universally prestarlike functions. J. Korean Math. Soc. 55(5), 1019–1030 (2018)

    MathSciNet  MATH  Google Scholar 

  2. Duren, P.L.: Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259. Springer, New York (1983)

    Google Scholar 

  3. Fekete, M., Szegö, G.: Eine Bemerkung über ungerade schlichte Funktionen. J. Lond. Math. Soc. 8, 85–89 (1933)

    Article  Google Scholar 

  4. Grenander, U., Szegö, G.: Toeplitz Forms and their Applications. University of California Press, Berkeley (1958)

    Book  Google Scholar 

  5. Janteng, A., Halim, S.A., Darus, M.: Hankel determinant for starlike and convex functions. Int. J. Math. Anal 1(13–16), 619–625 (2007)

    MathSciNet  MATH  Google Scholar 

  6. Libera, R.J., Zlotkiewicz, E.J.: Early coefficients of the inverse of a regular convex function. Proc. Am. Math. Soc. 85(2), 225–230 (1982)

    Article  MathSciNet  Google Scholar 

  7. Liu, M.S., Xu, J.F.G., Yang, M.: Upper bound of second Hankel determinant for certain subclasses of analytic functions. Abs. Appl. Anal. 603180, 10 (2014)

    MathSciNet  MATH  Google Scholar 

  8. Mendiratta, R., Nagpal, S., Ravichandran, V.: On a subclass of strongly starlike functions associated with exponential function. Bull. Malays. Math. Sci. Soc. 38, 365–386 (2015)

    Article  MathSciNet  Google Scholar 

  9. Noonan, J.W., Thomas, D.K.: On the second Hankel determinant of areally mean \(p\)-valent functions. Trans. Am. Math. Soc. 223(2), 337–346 (1976)

    MathSciNet  MATH  Google Scholar 

  10. Ruscheweyh, S.: Some properties of prestarlike and universally prestarlike functions. Int. Conf. Geom. Funct. Theory J. Anal. 15, 247–254 (2007)

    MathSciNet  MATH  Google Scholar 

  11. Ruscheweyh, S., Salinas, L.: Universally prestarlike functions as convolution multipliers. Math. Z. 263(3), 607–617 (2009)

    Article  MathSciNet  Google Scholar 

  12. Ruscheweyh, S., Salinas, L., Sugawa, T.: Completely monotone sequences and universally prestarlike functions. Isreal J. Math. 171, 285–304 (2009)

    Article  MathSciNet  Google Scholar 

  13. Ruscheweyh, S.: Convolutions in Geometric Function Theory, Sem. Math. Sup., vol. 83. Presses University, Montreal (1982)

    Google Scholar 

  14. Shanmugam, T.N., Lourthu Mary, J.: Properties of universally prestarlike functions. Int. J. Eng. Res. Tech. 1(10), 1–7 (2012)

  15. Shanmugam, T.N., Lourthu Mary, J.: A note on universally prestarlike functions. Stud. Univ. Babes Bolyai Math. 57(1), 53–60 (2012)

    MathSciNet  MATH  Google Scholar 

  16. Shanmugam, T.N., Lourthu Mary, J.: Fekete–Szeg ö inequality for Universally prestarlike functions. Fract. Calc. Appl. Anal. 13(14), 385–394 (2010)

    MathSciNet  MATH  Google Scholar 

  17. Srutha Keerthi, B., Revathi, M., Murugusundaramoorthy, G.: The second Hankel determinant for certain classes of analytic univalent functions. Int. J. Appl. Eng. Res. 9(22), 12241–12254 (2014)

    Google Scholar 

  18. Zhang, H.Y., Tang, H., Niu, X.M.: Third-order Hankel determinant for certain class of analytic functions related with exponential function. Symmetry 10, 501 (2018)

    Article  Google Scholar 

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Acknowledgements

The authors are grateful to the referees of this article, that gave valuable comments and advices,in order to revise and improve the results of the paper in the present form.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Dicle University, Diyarbakir, Turkey

    H. Özlem Güney

  2. Department of Mathematics, School of Advanced Sciences, Vellore Institute of technology, Vellore, Tamilnadu, 632014, India

    G. Murugusundaramoorthy & K. Vijaya

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  1. H. Özlem Güney
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  2. G. Murugusundaramoorthy
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  3. K. Vijaya
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Correspondence to G. Murugusundaramoorthy.

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(Dedicated to Prof. Stephan Ruscheweyh, Mathematisches Institut, Universita ẗ Wurzbur̈g, D-97074 Wurzburg, Germany).

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Güney, H.Ö., Murugusundaramoorthy, G. & Vijaya, K. Second Hankel determinant for universally prestarlike functions related with exponential function. Afr. Mat. 32, 685–694 (2021). https://doi.org/10.1007/s13370-020-00853-7

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  • DOI: https://doi.org/10.1007/s13370-020-00853-7

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