Bounds for radii of starlikeness and convexity of some special functions

Aktas I., BARİCZ A., ORHAN H.

TURKISH JOURNAL OF MATHEMATICS, cilt.42, sa.1, ss.211-226, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 42 Sayı: 1
  • Basım Tarihi: 2018
  • Doi Numarası: 10.3906/mat-1610-41
  • Dergi Adı: TURKISH JOURNAL OF MATHEMATICS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, TR DİZİN (ULAKBİM)
  • Sayfa Sayıları: ss.211-226
  • Anahtar Kelimeler: Lommel, Struve, and Bessel functions, univalent, starlike, and convex functions, radius of univalence, starlikeness, and convexity, zeros of Lommel, Struve, and Bessel functions, Mittag Leffler expansions, Laguerre POlya class of entire functions, NORMALIZED BESSEL-FUNCTIONS, 1ST KIND, GEOMETRIC-PROPERTIES
  • Atatürk Üniversitesi Adresli: Evet

Özet

In this paper we consider some normalized Bessel, Struve, and Lommel functions of the first kind and, by using the Euler Rayleigh inequalities for the first positive zeros of a combination of special functions, we obtain tight lower and upper bounds for the radii of starlikeness of these functions. By considering two different normalizations of Bessel and Struve functions we give some inequalities for the radii of convexity of the same functions. On the other hand, we show that the radii of univalence of some normalized Struve and Lommel functions are exactly the radii of starlikeness of the same functions. In addition, by using some ideas of Ismail and Muldoon we present some new lower and upper bounds for the zeros of derivatives of some normalized Struve and Lommel functions. The Laguerre Polya class of real entire functions plays an important role in our study.