Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CERTAIN SUBCLASSES OF ANALYTIC FUNCTIONS ASSOCIATED WITH THE CHEBYSHEV POLYNOMIALS

  • Received : 2017.10.18
  • Accepted : 2018.09.08
  • Published : 2018.12.25
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Abstract

In this paper, we obtain initial coefficient bounds for an unified subclass of analytic functions by using the Chebyshev polynomials. Furthermore, we find the Fekete-$Szeg{\ddot{o}}$ result for this class. All results are sharp. Consequences of the results are also discussed.

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References

  1. S. Altinkaya and S. Yalcin, On the Chebyshev polynomial bounds for classes of univalent functions, Khayyam J. Math. 2(1) (2016), 1-5.
  2. E. H. Doha, The First and second kind Chebyshev coeffcients of the moments of the general-order derivative of an infinitely differentiable function, Int. J. Comput. Math. 51 (1944), 21-35.
  3. J. Dziok, R. K. Raina and J. Sokol, Application of Chebyshev polynomials to classes of analytic functions, C. R. Math. Acad. Sci. Paris 353(5) (2015), 433-438. https://doi.org/10.1016/j.crma.2015.02.001
  4. J. C. Mason, Chebyshev polynomial approximations for the L-membrane eigenvalue problem, SIAM J. Appl. Math. 15 (1967), 172-186. https://doi.org/10.1137/0115014
  5. T. Whittaker and G. N. Watson, A course of modern analysis, reprint of the fourth edition (1927), Cambridge Mathematical Library, Cambridge Univ. Press, Cambridge, 1996.