Korean J. Math. Vol. 32 No. 1 (2024) pp.173-182
DOI: https://doi.org/10.11568/kjm.2024.32.1.173

Applications of the Gaussian hypergeometric function to some subclasses of analytic functions

Main Article Content

Abeer O. Badghaish
Amani Z. Bajamal


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

Article Details


[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. Google Scholar

[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. Google Scholar

[3] B. F. Hassan, A0n application of certain integral and differential operators, M. Sc. Thesis, Mansoura University, 2016. Google Scholar

[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 Google Scholar

[5] A. Y. Lashin, On a certain subclass of starlike functions with negative coefficients, J. Inequal. Pure Appl. Math. 10 (2009) (2), 1–8. Google Scholar

[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 Google Scholar

[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 Google Scholar

[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 Google Scholar

[9] G. I. Oros, New conditions for univalence of confluent hypergeometric function, Symmetry 13 (2021), 82. https://doi.org/10.3390/sym13010082 Google Scholar

[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 Google Scholar

[11] H. Silverman, Univalent functions with negative coefficients, Proc. Amer. Math. Soc. 51 (1) (1975), 109–116. Google Scholar

[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 Google Scholar