Advertisement

Chebyshev polynomial bounds for a certain subclass of univalent functions defined by Komatu integral operator

  • Şahsene AltınkayaEmail author
  • Sibel Yalçın
Article
  • 5 Downloads

Abstract

In this work, using the Komatu integral operator, we introduced a new subclass of univalent functions and using the Chebyshev polynomials, we obtain coefficient expansions for functions in this class.

Keywords

Chebyshev polynomials Analytic and univalent functions Coefficient bounds Subordination Komatu integral operator 

Mathematics Subject Classification

30C45 33C45 

Notes

References

  1. 1.
    Altınkaya, Ş., Yalçın, S.: On the Chebyshev polynomial bounds for classes of univalent functions. Khayyam J. Math. 2, 1–5 (2016)MathSciNetzbMATHGoogle Scholar
  2. 2.
    Darus, M., Thomas, D.K.: On the Fekete–Szegö theorem for close-to-convex functions. Math. Jpn. 44, 507–511 (1996)zbMATHGoogle Scholar
  3. 3.
    Darus, M., Thomas, D.K.: On the Fekete–Szegö theorem for close-to-convex functions. Math. Jpn. 47, 125–132 (1998)zbMATHGoogle Scholar
  4. 4.
    Dziok, J., Raina, R.K., Sokol, J.: Application of Chebyshev polynomials to classes of analytic functions. C. R. Acad. Sci. Paris Ser. I(353), 433–438 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Doha, E.H.: The first and second kind Chebyshev coefficients of the moments of the general-order derivative of an infinitely differentiable function. Int. J. Comput. Math. 51, 21–35 (1994)CrossRefzbMATHGoogle Scholar
  6. 6.
    Fekete, M., Szegö, G.: Eine bemerkung über ungerade schlichte funktionen. J. Lond. Math. Soc. 2, 85–89 (1933)CrossRefzbMATHGoogle Scholar
  7. 7.
    Kanas, S., Darwish, H.E.: Fekete–Szegö problem for starlike and convex functions of complex order. Appl. Math. Lett. 23, 777–782 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    Koepf, W.: On the Fekete–Szegö problem for close-to-convex functions. Proc. Am. Math. Soc. 101, 89–95 (1987)zbMATHGoogle Scholar
  9. 9.
    Komatu, Y.: On analytic prolongation of a family of operators. Mathematica (Cluj) 32, 141–145 (1990)MathSciNetzbMATHGoogle Scholar
  10. 10.
    Libera, R.J.: Some classes of regular univalent functions. Proc. Am. Math. Soc. 16, 755–758 (1965)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    London, R.R.: Fekete–Szegö inequalities for close-to-convex functions. Proc. Am. Math. Soc. 117, 947–950 (1993)zbMATHGoogle Scholar
  12. 12.
    Ma, W., Minda, D.: A unified treatment of some special classes of univalent functions. In: Li, Z., Ren, F., Yang, L., Zhang, S. (eds.) Proceedings of the Conference on Complex Analysis, pp. 157–169. International Press Inc., Boston (1992)Google Scholar
  13. 13.
    Mason, J.C.: Chebyshev polynomials approximations for the L-membrane eigenvalue problem. SIAM J. Appl. Math. 15, 172–186 (1967)MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Sãlãgean, G.S.: Subclasses of univalent functions. In: Complex Analysis—Fifth Romanian Finish Seminar, Bucharest, vol. 1, pp. 362–372 (1983)Google Scholar
  15. 15.
    Srivastava, H.M., Mishra, A.K., Das, M.K.: The Fekete–Szegö problem for a subclass of close-to-convex functions. Complex Var. Theory Appl. 44, 145–163 (2001)zbMATHGoogle Scholar
  16. 16.
    Whittaker, E.T., Watson, G.N.: A Course of Modern Analysis: An Introduction to the General Theory of Infinite Processes of Analytic Functions with an Account of the Principal Transcendental Function, 4th edn. Cambridge University Press, Cambridge (1963)Google Scholar

Copyright information

© African Mathematical Union and Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Arts and ScienceBursa Uludag UniversityBursaTurkey

Personalised recommendations