The Radius of \(\alpha \) -Convexity of Normalized Bessel Functions of the Fir

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• 作者：Árpád Baricz ; Halit Orhan ; Róbert Szász
• 关键词：Bessel functions ; Convex ; starlike and \(\alpha \) ; convex functions ; Zeros of Bessel functions
• 刊名：Computational Methods and Function Theory
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：16
• 期：1
• 页码：93-103
• 全文大小：515 KB
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  4.Baricz, Á., Kupán, P.A., Szász, R.: The radius of starlikeness of normalized Bessel functions of the first kind. Proc. Am. Math. Soc. 142(6), 2019–2025 (2014)CrossRef MATH
  5.Baricz, Á., Ponnusamy, S.: Starlikeness and convexity of generalized Bessel functions. Integr. Transforms Spec. Funct. 21, 641–653 (2010)CrossRef MathSciNet MATH
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  13.Mocanu, P.T., Reade, M.O.: The radius of \(\alpha \) -convexity for the class of starlike univalent functions, \(\alpha \) real. Proc. Am. Math. Soc. 51(2), 395–400 (1975)MathSciNet MATH
  14.Olver, F.W.J., Lozier, D.W., Boisvert, R.F., Clark, C.W. (eds.): NIST handbook of mathematical functions. Cambridge Univ. Press, Cambridge (2010)MATH
  15.Szász, R.: On starlikeness of Bessel functions of the first kind. In: Proceedings of the 8th Joint Conference on Mathematics and Computer Science, Komárno, Slovakia, p 9 (2010)
  16.Szász, R., Kupán, P.A.: About the univalence of the Bessel functions. Stud. Univ. Babeş-Bolyai Math. 54(1), 127–132 (2009)MATH
  17.Watson, G.N.: A treatise of the theory of Bessel functions. Cambridge University Press, Cambridge (1995)MATH
  
• 作者单位：Árpád Baricz (1) (2)
  Halit Orhan (3)
  Róbert Szász (4)
  
  1. Department of Economics, Babeş-Bolyai University, 400591, Cluj-Napoca, Romania
  2. Institute of Applied Mathematics, Óbuda University, Budapest, 1034, Hungary
  3. Department of Mathematics, Faculty of Science, Atatürk University, 25240, Erzurum, Turkey
  4. Department of Mathematics and Informatics, Sapientia Hungarian University of Transylvania, 540485, Târgu-Mureş, Romania
  
• 刊物主题：Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable;
• 出版者：Springer Berlin Heidelberg
• ISSN：2195-3724

文摘

The radii of \(\alpha \)-convexity are deduced for three different kinds of normalized Bessel functions of the first kind and it is shown that these radii are between the radii of starlikeness and convexity, when \(\alpha \in [0,1]\), and they are decreasing with respect to the parameter \(\alpha \). The results presented in this paper unify some recent results on the radii of starlikeness and convexity for normalized Bessel functions of the first kind. The key tools in the proofs are some interlacing properties of the zeros of some Dini functions and the zeros of Bessel functions of the first kind.