DOI QR코드

DOI QR Code

APPLICATIONS OF THE GAUSSIAN HYPERGEOMETRIC FUNCTION TO SOME SUBCLASSES OF ANALYTIC FUNCTIONS

  • Abeer O. Badghaish (Department of Mathematics, Faculty of Science, King Abdulaziz, University) ;
  • Amani Z. Bajamal (Department of Mathematics, Faculty of Science, King Abdulaziz, University)
  • Received : 2024.01.09
  • Accepted : 2024.02.10
  • Published : 2024.03.30

Abstract

In this paper, we derive the necessary and sufficient conditions for the Gaussian hypergeometric function to be in some subclasses of analytic functions.

Keywords

Acknowledgement

The authors would like to thank Prof. Abdel Moneim Y. Lashin for his support and valuable contribution in this research.

References

  1. M. K. Aouf, A. O. Mostafa and H. M. Zayed, Some properties of uniformly starlike and convex hypergeometric functions, Azerbaijan J. Math. 9 (2) (2019), 3-19.
  2. N. E. Cho, S. Y. Woo and S. Owa, Uniform convexity properties for hypergeometric functions, Fract. Calc. Appl. Anal. 5 (2002) (3), 303-314.
  3. B. F. Hassan, A0n application of certain integral and differential operators, M. Sc. Thesis, Mansoura University, 2016.
  4. O. S. Kwon and N. E. Cho, Starlike and convex properties for hypergeometric functions, Internat. J. Math. Math. Sci. 2008 (2008), Art. ID 159029, 11 Pages. https://doi.org/10.1155/2008/159029
  5. A. Y. Lashin, On a certain subclass of starlike functions with negative coefficients, J. Inequal. Pure Appl. Math. 10 (2009) (2), 1-8.
  6. A. O. Mostafa, Starlikeness and convexity results for hypergeometric functions, Comput. Math. Appl. 59 (2010), 2821-2826. https://doi.org/10.1016/j.camwa.2010.01.053
  7. R. Nusrat, S. A. Eman and J. Abu, On starlikeness and convexity properties of the generalized Bessel-hypergeometric function, Indian J. Industrial Appl. Math. 10 (2019), 182-201. https://doi.org/10.5958/1945-919X.2019.00013.6
  8. H. Orhan, On a subclass of analytic functions with negative coefficients, Appl. Math. Comput. 142 (2003), 243-253. https://doi.org/10.1016/S0096-3003(02)00299-0
  9. G. I. Oros, New conditions for univalence of confluent hypergeometric function, Symmetry 13 (2021), 82. https://doi.org/10.3390/sym13010082
  10. C. Ramachandran, L. Vanitha and G. Murugusundaramoorthy, Starlike and uniformly convex functions involving generalized hypergeometric function, Internat. J. Pure Appl. Math. 92 (5) (2014), 691-701. http://dx.doi.org/10.12732/ijpam.v92i5.5
  11. H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1) (1975), 109-116.
  12. H. Silverman, Starlike and convexity properties for hypergeometric functions, J. Math. Anal. Appl. 172 (1993) (2), 574-581. https://doi.org/10.1006/jmaa.1993.1044