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COEFFICIENT ESTIMATES FOR GENERALIZED LIBERA TYPE BI-CLOSE-TO-CONVEX FUNCTIONS

  • Serap, Bulut (Kocaeli University Faculty of Aviation and Space Sciences)
  • 투고 : 2022.04.25
  • 심사 : 2022.10.25
  • 발행 : 2022.12.30

초록

In a recent paper, Sakar and Güney introduced a new class of bi-close-to-convex functions and determined the estimates for the general Taylor-Maclaurin coefficients of functions therein. The main purpose of this note is to give a generalization of this class. Also we point out the proof by Sakar and Güney is incorrect and present a correct proof.

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참고문헌

  1. O. Altintas, H. Irmak, S. Owa and H.M. Srivastava, Coefficient bounds for some families of starlike and convex functions of complex order, Appl. Math. Letters 20 (2007), 1218-1222.  https://doi.org/10.1016/j.aml.2007.01.003
  2. H. Airault and A. Bouali, Differential calculus on the Faber polynomials, Bull. Sci. Math. 130 (2006), 179-222.  https://doi.org/10.1016/j.bulsci.2005.10.002
  3. H. Airault and J. Ren, An algebra of differential operators and generating functions on the set of univalent functions, Bull. Sci. Math. 126 (2002), 343-367.  https://doi.org/10.1016/S0007-4497(02)01115-6
  4. D.A. Brannan and T.S. Taha, On some classes of bi-univalent functions, Studia Univ. Babes-Bolyai Math. 31 (2) (1986), 70-77. 
  5. S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions, C. R., Math., Acad. Sci. Paris 352 (6) (2014), 479-484.  https://doi.org/10.1016/j.crma.2014.04.004
  6. S. Bulut, Faber polynomial coefficient estimates for a subclass of analytic bi-univalent functions, Filomat 30 (6) (2016), 1567-1575.  https://doi.org/10.2298/FIL1606567B
  7. S. Bulut, A new comprehensive subclass of analytic bi-close-to-convex functions, Turk. J. Math. 43 (3) (2019), 1414-1424.  https://doi.org/10.3906/mat-1902-21
  8. S. Bulut, Coefficient estimates for Libera type bi-close-to-convex functions, Mathematica Slovaca 71 (6) (2021), 1401-1410.  https://doi.org/10.1515/ms-2021-0060
  9. S. Bulut, Coefficient estimates for functions associated with vertical strip domain, Commun. Korean Math. Soc. 37 (2) (2022), 537-549. 
  10. P.L. Duren, Univalent Functions, Grundlehren der Mathematischen Wissenschaften, vol. 259, Springer, New York, 1983. 
  11. G. Faber, Uber polynomische Entwickelungen , Math. Ann. 57 (3) (1903) 389-408.  https://doi.org/10.1007/BF01444293
  12. H.O. Guney, G. Murugusundaramoorthy and H.M. Srivastava, The second Hankel determinant for a certain class of bi-close-to-convex functions, Result. Math. 74 (3) (2019), Paper No. 93. 
  13. S.G. Hamidi and J.M. Jahangiri, Faber polynomial coefficient estimates for analytic bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 352 (2014), 17-20.  https://doi.org/10.1016/j.crma.2013.11.005
  14. S.G. Hamidi and J.M. Jahangiri, Faber polynomial coefficient estimates for bi-univalent functions defined by subordinations, Bull. Iran. Math. Soc. 41 (5) (2015), 1103-1119. 
  15. J.M. Jahangiri and S.G. Hamidi, Coefficient estimates for certain classes of bi-univalent functions, Int. J. Math. Math. Sci. 2013, Art. ID 190560, 4 pp. 
  16. J.M. Jahangiri, S.G. Hamidi and S.A. Halim, Coefficients of bi-univalent functions with positive real part derivatives, Bull. Malays. Math. Sci. Soc. (2) 37 (3) (2014), 633-640. 
  17. W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169-185 (1953). 
  18. R.J. Libera, Some radius of convexity problems, Duke Math. J. 31 (1964), 143-158.  https://doi.org/10.1215/S0012-7094-64-03114-X
  19. Ch. Pommerenke, Univalent Functions, Vandenhoeck and Rupercht, Gottingen, 1975. 
  20. M.S. Robertson, On the theory of univalent functions, Ann. of Math. (Ser. 1) 37 (1936), 374-408.  https://doi.org/10.2307/1968451
  21. F.M. Sakar and H.O. Guney, Coefficient bounds for a new subclass of analytic bi-close-to-convex functions by making use of Faber polynomial expansion, Turkish J. Math. 41 (2017), 888-895.  https://doi.org/10.3906/mat-1605-117
  22. F.M. Sakar and H.O. Guney, Faber polynomial coefficient bounds for analytic bi-close-to-convex functions defined by fractional calculus, J. Fract. Calc. Appl. 9 (1) (2018), 64-71. 
  23. H.M. Srivastava and S.M. El-Deeb, The Faber polynomial expansion method and the Taylor-Maclaurin coefficient estimates of bi-close-to-convex functions connected with the q-convolution, AIMS Math. 5 (6) (2020), 7087-7106.  https://doi.org/10.3934/math.2020454
  24. H.M. Srivastava, A.K. Mishra and P. Gochhayat, Certain subclasses of analytic and bi-univalent functions, Appl. Math. Lett. 23 (2010) 1188-1192.  https://doi.org/10.1016/j.aml.2010.05.009
  25. P.G. Todorov, On the Faber polynomials of the univalent functions of class Σ, J. Math. Anal. Appl. 162 (1991), 268-276.  https://doi.org/10.1016/0022-247x(91)90193-4
  26. Z.-G. Wang and S. Bulut, A note on the coefficient estimates of bi-close-to-convex functions, C. R. Acad. Sci. Paris, Ser. I 355 (2017), 876-880.  https://doi.org/10.1016/j.crma.2017.07.014
  27. A. Zireh, E.A. Adegani and S. Bulut, Faber polynomial coefficient estimates for a comprehensive subclass of analytic bi-univalent functions defined by subordination, Bull. Belg. Math. Soc.-Simon Stevin 23 (4) (2016), 487-504.