대한수학회논문집 (Communications of the Korean Mathematical Society)

  • 제39권2호
  • /
  • Pages.461-470
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  • 2024
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  • 1225-1763(pISSN)
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  • 2234-3024(eISSN)
대한수학회 (Korean Mathematical Society)
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HORADAM POLYNOMIALS FOR A NEW SUBCLASS OF SAKAGUCHI-TYPE BI-UNIVALENT FUNCTIONS DEFINED BY (p, q)-DERIVATIVE OPERATOR

  • 투고 : 2023.10.24
  • 심사 : 2024.02.01
  • 발행 : 2024.04.30
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초록

In this paper, a new subclass, 𝒮𝒞𝜇,p,q𝜎 (r, s; x), of Sakaguchitype analytic bi-univalent functions defined by (p, q)-derivative operator using Horadam polynomials is constructed and investigated. The initial coefficient bounds for |a2| and |a3| are obtained. Fekete-Szegö inequalities for the class are found. Finally, we give some corollaries.

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참고문헌

  1. S. Baskaran, G. Saravanan, and B. Vanithakumari, Sakaguchi type function defined by (p, q)-fractional operator using Laguerre polynomials, Palest. J. Math. 11 (2022), Special Issue II, 41-47.
  2. S. Baskaran, G. Saravanan, S. Yal,cn, and B. Vanithakumari, Sakaguchi type function defined by (p, q)-derivative operator using gegenbauer polynomials, Int. J. Nonlinear Analy. Appl. 13 (2022), no. 2, 2197-2204.
  3. R. P. Boas, Aspects of contemporary complex analysis, Academic Press, Inc., London, 1980.
  4. L. I. Cotirla and A. K. Wanas, Applications of Laguerre polynomials for Bazilevic and θ-pseudo-starlike bi-univalent functions associated with Sakaguchi-type functions, Symmetry 15 (2023), no. 2, 406.
  5. B. A. Frasin, Coefficient inequalities for certain classes of Sakaguchi type functions, Int. J. Nonlinear Sci. 10 (2010), no. 2, 206-211.
  6. A. F. Horadam, Jacobsthal representation polynomials, Fibonacci Quart. 35 (1997), no. 2, 137-148.
  7. A. F. Horadam and J. M. Mahon, Pell and Pell-Lucas polynomials, Fibonacci Quart. 23 (1985), no. 1, 7-20.
  8. T. Horzum and E. G. Ko,cer, On some properties of Horadam polynomials, Int. Math. Forum 4 (2009), no. 25-28, 1243-1252.
  9. T. Koshy, Fibonacci and Lucas Numbers with Applications. Vol. 2, Pure and Applied Mathematics (Hoboken), John Wiley & Sons, Inc., Hoboken, NJ, 2019.
  10. M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc. 18 (1967), 63-68. https://doi.org/10.2307/2035225
  11. A. Lupas, A guide of Fibonacci and Lucas polynomials, Octogon Math. Mag. 7 (1999), no. 1, 3-12.
  12. K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75. https://doi.org/10.2969/jmsj/01110072
  13. G. Saravanan and K. Muthunagai, Co-efficient estimates for the class of bi-quasi-convex functions using faber polynomials, Far East J. Math. Sci. (FJMS) 102 (2017), no. 10, 2267-2276. https://doi.org/10.17654/MS102102267
  14. G. Saravanan and K. Muthunagai, Estimation of upper bounds for initial coefficients and fekete-szego inequality for a subclass of analytic bi-univalent functions, In Applied Mathematics and Scientific Computing: International Conference on Advances in Mathematical Sciences, Vellore, India, December 2017-Volume II, pages 57-65. Springer, 2019.
  15. G. Szego, Orthogonal Polynomials, American Mathematical Society Colloquium Publications, Vol. 23, Amer. Math. Soc., New York, 1939.
  16. G. Szego, Orthogonal polynomials, fourth edition, American Mathematical Society Colloquium Publications, Vol. XXIII, Amer. Math. Soc., Providence, RI, 1975.
  17. R. Vijaya, T. V. Sudharsan, and S. Sivasubramanian, Coefficient estimates for certain subclasses of biunivalent functions defined by convolution, Int. J. Anal. 2016 (2016), Art. ID 6958098, 5 pp. https://doi.org/10.1155/2016/6958098
  18. A. K. Wanas, F. M. Sakar, and A. A. Lupa,s, Applications Laguerre polynomials for families of bi-univalent functions defined with (p, q)-Wanas operator, Axioms 12 (2023), no. 5, 430.
  19. A. K. Wanas, G. S. Salagean, and A. P.-S. Orsolya, Coefficient bounds and Fekete-Szego inequality for a certain family of holomorphic and bi-univalent functions defined by (M, N)-Lucas polynomials, Filomat 37 (2023), no. 4, 1037-1044. https://doi.org/10.2298/fil2304037w
  20. Q.-H. Xu, Y.-C. Gui, and H. M. Srivastava, Coefficient estimates for a certain subclass of analytic and bi-univalent functions, Appl. Math. Lett. 25 (2012), no. 6, 990-994. https://doi.org/10.1016/j.aml.2011.11.013
  21. S. Yalcin, K. Muthunagai, and G. Saravanan, A subclass with bi-univalence involving (p, q)-Lucas polynomials and its coefficient bounds, Bol. Soc. Mat. Mex. (3) 26 (2020), no. 3, 1015-1022. https://doi.org/10.1007/s40590-020-00294-z