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Fekete–Szegö problem for a class of \(\lambda \)-convex and \(\mu \)-starlike functions associated with k-th root transformation using quasi-subordination

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Abstract

In this paper, we obtain the estimates with k-th root transformation for certain classes of analytic univalent functions using quasi-subordination. Some interesting remarks of the results presented here are also discussed.

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References

  1. Ali, R.M., Lee, S.K., Ravichandran, V., Supramaniam, S.: The Fekete–Szegő coefficient functional for transforms of analytic functions. Bull. Iran Math. Soc. 35(2), 119–142 (2009)

    MATH  Google Scholar 

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

    MATH  Google Scholar 

  3. El-Ashwah, R., Kanas, S.: Fekete–Szegö inequalities for quasi-subordination functions classes of complex order. Kyungpook Math. J. 55(3), 679–688 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  4. Gurusamy, P., Sokół, J., Sivasubramanian, S.: The Fekete–Szegö functional associated with \(k\)-th root transformation using quasi-subordination. C. R. Math. Acad. Sci. Paris. 353(7), 617–622 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  5. Goyal, S.P., Singh, O.: Fekete–Szego problems and coefficient estimates of quasi-subordination classes. J. Rajasthan Acad. Phys. Sci. 13(2), 133–142 (2014)

    MathSciNet  MATH  Google Scholar 

  6. Haji Mohd, M., Darus, M.: Fekete-Szegő problems for quasi-subordination classes. Abstr. Appl. Anal. 2012, 192956 (2012). https://doi.org/10.1155/2012/192956

  7. Keogh, F.R., Merkes, E.P.: A coefficient inequality for certain classes of analytic functions. Proc. Am. Math. Soc. 20, 8–12 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  8. Ma, W.C., Minda, D.: A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Lang, L., Zhang, S. (eds.) Proceedings of the Conference on Complex Analysis, pp 157–169. International Press, Cambridge, Mass, USA (1992)

  9. Magesh, N., Balaji, V.K., Yamini, J.: Certain subclasses of bistarlike and biconvex functions based on quasi-subordination. Abstr. Appl. Anal. 2016, 3102960 (2016). https://doi.org/10.1155/2016/3102960

  10. Magesh, N., Yamini, J.: Fekete–Szegö inequalities associated with \(k\)th root transformation based on quasi-subordination. Ann. Univ. Paedagog. Crac. Stud. Math. 16, 7–15 (2017)

    MathSciNet  MATH  Google Scholar 

  11. Miller, S.S., Mocanu, P.T., Reade, M.O.: All \(\alpha \)-convex functions are starlike. Rev. Roumaine Math. Pure. Appl. 17, 1395–1397 (1972)

    MathSciNet  MATH  Google Scholar 

  12. Orhan, H., Magesh, N., Yamini, J.: Coefficient estimates for a class of bi-univalent functions associated with quasi-subordination. Creat. Math. Inform. 26(2), 193–199 (2017)

    MathSciNet  MATH  Google Scholar 

  13. Robertson, M.S.: Quasi-subordination and coefficient conjectures. Bull. Am. Math. Soc. 76, 1–9 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  14. Xiaofei, L.: On the Fekete–Szegö problem for a subclass of \(\lambda \)-convex functions. Int. J. Math. Res. 5(1), 13–17 (2013)

    Google Scholar 

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Acknowledgements

The authors are very much thankful to the editor-in-chief and the anonymous referees for their comments and suggestions on this paper.

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Authors and Affiliations

  1. Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri, Tamilnadu, 635001, India

    N. Magesh

  2. Department of Mathematics, L. N. Govt College, Ponneri, Chennai, Tamilnadu, India

    V. K. Balaji

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  1. N. Magesh
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  2. V. K. Balaji
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Correspondence to N. Magesh.

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All authors jointly worked on the results and they read and approved the final manuscript.

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Magesh, N., Balaji, V.K. Fekete–Szegö problem for a class of \(\lambda \)-convex and \(\mu \)-starlike functions associated with k-th root transformation using quasi-subordination. Afr. Mat. 29, 775–782 (2018). https://doi.org/10.1007/s13370-018-0575-3

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  • DOI: https://doi.org/10.1007/s13370-018-0575-3

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