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Results on Hankel Determinants for the Class of Univalent Functions with a Generalized Derivative Operator

Author Affiliations

  • 1Mathematics Department, Faculty of Science -Al-Khomus, Al-Margib University, Libya
  • 2Mathematics Department, Faculty of Education of Benghazi, University of Benghazi, Libya
  • 3School of Mathematical Sciences, Faculty of Science and Technology Universiti Kebangsaan Malaysia

Res. J. Mathematical & Statistical Sci., Volume 13, Issue (2), Pages 8-11, May,12 (2025)

Abstract

In this article, we introduce a new subclass of analytic functions defined by a generalized generalized derivative operator. The Hankel determinant for the nonlinear functional is obtained. Our result extends corresponding previously known result.

References

  1. Duren, P. L. (1983)., Univalent Functions Grundlehren der Mathematischen Wissenschaften., Springer-Verlag, New York, 259.
  2. Noor K. (1993)., Hankel determinant problem for the class of functions with bounded boundary rotation., Rev. Roum. Math. Pures Et Appl, 28(8), 731-739.
  3. Ehrenborg R. (2000)., The Hankel determinant of exponential polynomials., American Mathematical Monthly, 107, 557-560 .
  4. Layman J. W. (2001)., The Hankel transform and some of its properties., J. of Integer Sequences, 4, 1-11.
  5. Janteng A., Halim S. & Darus M. (2006)., Coefficient inequality for a function whose derivative has a positive real part., J. Ineq. Pure and Appl. Math., 7, 1-5.
  6. Janteng A., Halim S.A. and Darus M. (2007)., Hankel Determinant for starlike and convex functions., Int J. Math Anal; 1, 619-625.
  7. Lee S. K., Ravichandran V. and Supramaniam S. (2013)., Bounds for the second Hankel determinant of certain univalent functions., J Inequal Appl; 281.
  8. Kund S. N. & Mishra A. K. (2013)., The second Hankel determinant for a class of analytic functions associated with the Carlson-Shaffer operator., Tamkang J. Math., 44(1), 73–82.
  9. Amer A. A. (2016)., Second Hankel Determinant for New Subclass Defined by a Linear Operator, Springer., International Publishing Switzerland, Chapter 6.
  10. Alabbar N., Alkabaily S. & Amer A. A. (2024)., Hankel determinant problem for a new subclass of analytic functions defined by integral operator associated with the Hurwitz-Lerch zeta., The academic open journal of applied and human sciences, 5(2), 2709-3344.
  11. Alkabaily S. & Alabbar N. (2020)., Hankel determinant for certain subclasses of analytic functions associated with generalized Srivastava-atria operator., Journal of applied Science, 4, 1-9.
  12. Noonan J. & Thomas D. (1976)., On the second Hankel determinant of areally mean p. valent functions., Trans. Amer. Math. Soc., 223, 337-346.
  13. Amer A. A. & Darus M. (2011)., On some properties for new generalized derivative operator., Jordan Journal of Mathematics and Statistics, 4, 91-101.
  14. Shmella E. & Amer A. A. (2023)., Estimation of the Bounds of Univalent Functional of Coefficients Apply the Subordination Method., The Academic Open Journal of Applied and Human Sciences, 5(1), 2709-3344.
  15. Amer A. A. & Maslina M. (2012)., Some Properties of the Class of Univalent Functions with Negative Coefficients., Applied Mathematics, 3, 1851-1856.
  16. Alabbar N. M. & Amer A. A. (2017)., Properties of Generalized Derivative Operator to a Certain Subclass of Analytic Functions with Negative Coefficients., Global Libyan Journal, 2.
  17. Amer A. A. (2018)., On Subclasses Of Uniformly Bazilevic Type Functions Using New Generalized Derivative Operator., Special Issue for The 2nd Annual Conference on Theories and Applications of Basic and Biosciences.
  18. MacGregor T. H. (1962)., Functions whose derivative has a positive real part., Trans. Amer. Math. Soc, 104, 532- 537.
  19. Goodman A. W. (1957)., Univalent functions and nonanalytic curves., Proc. Amer. Math. Soc, 8, 598-60.
  20. Libera. R. J. & Z otkiewicz. E. J. (1983)., Coefficient bounds for the inverse of a function with derivative in P., Proceedings of the American Mathematical Society, 78, 251-257.
  21. Murugusundaramoorthy G. & Magesh N. (2009)., Coefficient inequalitties for certain classes of analytic functions associated with hankel determinant., Bulletin of Mathematical Analysis and Applications, 1, 85-89.
  22. Alabbar N., Darus M. & Amer A. A. (2023)., Coefficient Inequality and Coefficient Bounds for a New Subclass of Bazilevic Functions., Journal of Humanitarian and Applied Sciences, 8(23), 496-506.
  23. Amer A. A. and Ajaib S. K. (2018)., Some Inclusion Relationships for Certain Subclasses of Functions Associated With The Linear Fractional Differential Operator., Aperiodic Scientific Evaluated Journal, 10th.
  24. Amer A. A., Darus M. and Alabbar N. M. (2024). Properties for Generalized Starlike and Convex Functions of Order α., Fezzan University Scientific Journal, 3(1), 423-429., undefined
  25. Amer A. A., Darus M. and Alabbar N. M. (2024)., Necessary conditions for the generalized derivative operator in classes of univalent functions., Academy Journal for Basic and Applied Sciences, 6(2), 1-15.
  26. Abufares F. A. and Amer A. A. (2024)., Certain Applications of Analytic Functions Associated in Complex BB Differential Equations., Journal of the Faculty of Education Tripoli, 19(1), 264-274.
  27. Alsait A. A. and Alabbar N. M. (2019)., Fekete-Szego Problem for Starlike of Complex functions of Order Related to Generalized Derivative Operator., Journal of Humanities and applied Science, 4(8), 321-331.