• Deniz, Erhan (Department of Mathematics, Kafkas University) ;
  • Goren, Seyma (Department of Mathematics, Kafkas University)
  • Received : 2018.05.22
  • Accepted : 2019.01.14
  • Published : 2019.03.25


In this paper our aim is to establish some geometric properties (like starlikeness, convexity and close-to-convexity) for the generalized and normalized Dini functions. In order to prove our main results, we use some inequalities for ratio of these functions in normalized form and classical result of Fejer.


Supported by : Kafkas University


  1. A. Baricz, Geometric properties of generalized Bessel functions, Publ. Math. Debrecen 73(1-2) (2008), 155-178.
  2. A. Baricz and S. Ponnusamy, Starlikeness and convexity of generalized Bessel functions, Integr. Transforms Spec. Funct. 21 (2010), 641-653.
  3. A. Baricz, M. Caglar and E. Deniz, Starlikeness of Bessel functions and their derivatives, Math. Ineq. Appl. 19(2) (2016), 439-449.
  4. A. Baricz, E. Deniz and N. Yagmur, Close-to-convexity of normalized Dini functions, Math. Narch. 289 (2016), 1721-1726.
  5. A. Baricz. S. Ponnusamy and S. Singh, Modified Dini functions: monotonicity patterns and functional inequalities, Acta Math. Hungrica 149 (2016), 120-142.
  6. E. Deniz, H. Orhan and H. M. Srivastava, Some sufficient conditions for univalence of certain families of integral operators involving generalized Bessel functions, Taiwanese J. Math. 15(2) (2011), 883-917.
  7. E. Deniz, S. Goren and M. Caglar, Starlikeness and convexity of the generalized Dini functions, AIP Conference Proceedings 1833(020004) (2017), doi: 10.1063/1.4981652.
  8. L. Fejer, Untersuchungen uber Potenzreihen mit mehrfach monotoner Koeffizientenfolge, Acta Litterarum ac Scientiarum 8 (1936), 89-115.
  9. T. H. MacGregor, A class of univalent functions, Proc. Amer. Math. Society, 15 (1964), 311-317.
  10. S. Owa, M. Nunokawa, H. Saitoh and H. M. Srivastava, Close-to-convexity, starlikeness, and convexity of certain analytic functions, Appl. Math. Lett. 15 (2002), 63-69.
  11. G. N. Watson, A treatise on the theory of Bessel functions, Second edition, Cambridge University Press, Cambridge, London and New York, 1944.