Kyungpook Mathematical Journal

  • 제62권2호
  • /
  • Pages.257-269
  • /
  • 2022
  • /
  • 1225-6951(pISSN)
  • /
  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
권호 표지
DOI QR코드

DOI QR Code

Coefficient Estimates for a Subclass of Bi-univalent Functions Associated with Symmetric q-derivative Operator by Means of the Gegenbauer Polynomials

  • Amourah, Ala (Department of Mathematics, Faculty of Science and Technology, Irbid National University) ;
  • Frasin, Basem Aref (Faculty of Science, Department of Mathematics, Al al-Bayt University) ;
  • Al-Hawary, Tariq (Department of Applied Science, Ajloun College, Al-Balqa Applied University)
  • 투고 : 2021.07.03
  • 심사 : 2021.11.16
  • 발행 : 2022.06.30
PDF 다운로드
⟨ 이전 논문 다음 논문 ⟩

초록

In the present paper, a subclass of analytic and bi-univalent functions is defined using a symmetric q-derivative operator by means of Gegenbauer polynomials. Coefficients bounds for functions belonging to this subclass are obtained. Furthermore, the Fekete-Szegö problem for this subclass is solved. A number of known or new results are shown to follow upon specializing the parameters involved in our main results.

키워드

과제정보

The authors would like to thank the referees for their helpful comments and suggestions.

참고문헌

  1. I. Aldawish, T. Al-Hawary and B. A. Frasin, Subclasses of bi-univalent functions defined by Frasin differential operator, Afr. Mat., 30(3-4)(2019), 495-503. https://doi.org/10.1007/s13370-019-00662-7
  2. H. Aldweby and M. Darus, Some subordination results on q-analogue of Ruscheweyh differential operator, Abstr. Appl. Anal., 2014(2014), 6pp.
  3. S. Altinkaya and S. Yal,cin, Estimates on coefficients of a general subclass of biunivalent functions associated with symmetric q-derivative operator by means of the Chebyshev polynomials, Asia Pac. J. Math., 4(2)(2017), 90-99.
  4. A. Amourah, B. A. Frasin and T. Abdeljawad, Fekete-Szego inequality for analytic and bi-univalent functions subordinate to Gegenbauer polynomials, J. Funct. Spaces, 2021, 7 pp.
  5. A. Amourah, B. Frasin and G. Murugusundaramoorthy and T. Hawary, Bi-Bazilevic functions of order ϑ + iδ associated with (p, q)-Lucas polynomials, AIMS Mathematics, 6(5)(2021), 4296-4305. https://doi.org/10.3934/math.2021254
  6. A. Amourah, T. Al-Hawary and B. Frasin, Application of Chebyshev polynomials to certain class of bi-Bazilevic functions of order α+iβ, Afr. Mat., 32(2021), 1059-1066. https://doi.org/10.1007/s13370-021-00881-x
  7. H. Bateman, Higher Transcendental Functions, McGraw-Hill(1953).
  8. K. L. Brahim and Y. Sidomou, On some symmetric q-special functions, Matematiche(Catania), 68(2)(2013),107-122.
  9. D. A. Brannan and J. G. Clunie, Aspects of contemporary complex analysis , Academic Press, New York and London(1980).
  10. D. A. Brannan, and T. S. Taha, On some classes of bi-univalent functions, KFAS Proc. Ser., 3, Pergamon, Oxford(1988).
  11. B. Doman, The classical orthogonal polynomials, World Scientific(2015).
  12. M. Fekete and G. Szego, Eine Bemerkung Aber ungerade schlichte Funktionen, J. London Math. Soc., 1(2)(1933), 85-89. https://doi.org/10.1112/jlms/s1-2.2.85
  13. B. A. Frasin and M. K. Aouf, New subclasses of bi-univalent functions, Appl. Math. Lett., 24(2011), 1569-1573. https://doi.org/10.1016/j.aml.2011.03.048
  14. G. Gasper and M. Rahman, Basic Hypergeometric Series, Cambridge Univ. Press, Cambridge, MA(1990).
  15. F. H. Jackson, On q-functions and a certain difference operator, Trans. Royal Soc. Edinburgh, 46(1908), 253-281. https://doi.org/10.1017/S0080456800002751
  16. S. Kanas and D. Raducanu, Some subclass of analytic functions related to conic domains, Math. Slovaca, 64(5)(2014), 1183-1196. https://doi.org/10.2478/s12175-014-0268-9
  17. K. Kiepiela, I. Naraniecka and J. Szynal, The Gegenbauer polynomials and typically real functions, J. Comput. Appl. Math., 153(1-2)(2003), 273-282. https://doi.org/10.1016/S0377-0427(02)00642-8
  18. A. Legendre, Recherches sur laattraction des spheroides homogenes, Universittsbibliothek Johann Christian Senckenberg, 10(1785), 411-434.
  19. M. Lewin, On a coefficient problem for bi-univalent functions, Proc. Amer. Math. Soc., 18(1967), 63-68. https://doi.org/10.1090/S0002-9939-1967-0206255-1
  20. A. Mohammed and M. Darus, A generalized operator involving the q-hypergeometric function, Mat. Vesnik, 65(4)(2013), 454-465.
  21. G. Murugusundaramoorthy, N. Magesh and V. Prameela, Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., 2013, Art. ID 573017, 3 pp.
  22. E. Netanyahu, The minimal distance of the image boundary from the origin and the second coefficient of a univalent function in |ξ| < 1, Arch. Rational Mech. Anal., 32(1969), 100-112. https://doi.org/10.1007/BF00247676
  23. C. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, Gottingen(1975).
  24. C. Ramachandran, T. Soupramanien and B. A. Frasin,New subclasses of analytic function associated with q-difference operator, Eur. J. Pure Appl. Math., 10(2)(2017), 348-362.
  25. M. Reimer, Multivariate polynomial approximation, Birkh Auser(2012).
  26. T. M. Seoudy and M. K. Aouf, Coefficient estimates of new classes of q-starlike and q-convex functions of complex order, J. Math. Inequal., 10(1)(2016), 135-145.
  27. 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
  28. H. M. Srivastava, Operators of basic (or q-) calculus and fractional q-calculus and their applications in geometric function theory of complex analysis, Iran. J. Sci. Technol. Trans. A., 44(3)(2020), 327-344. https://doi.org/10.1007/s40995-019-00815-0
  29. T. S. Taha, Topics in Univalent Function Theory, Ph. D. Thesis, University of London(1981).
  30. F. Yousef, S. Alroud and M. Illafe, A comprehensive subclass of bi-univalent functions associated with Chebyshev polynomials of the second kind, Bol. Soc. Mat. Mex.(3), 26(2)(2020), 329-339. https://doi.org/10.1007/s40590-019-00245-3
  31. F. Yousef, B. A. Frasin and T. Al-Hawary, Fekete-Szego inequality for analytic and bi-univalent functions subordinate to Chebyshev polynomials, Filomat, 32(9)(2018), 3229-3236. https://doi.org/10.2298/fil1809229y