### Abstract

The goal of the present chapter is to study some geometric properties (like univalence, starlikeness, convexity, close-to-convexity) of generalized Bessel functions of the first kind. In order to achieve our goal we use several methods: differential subordinations technique, Alexander transform, results of L. Fejér, W. Kaplan, S. Owa and H.M. Srivastava, S. Ozaki, S. Ponnusamy and M. Vuorinen, H. Silverman, and Jack’s lemma. Moreover, we present some immediate applications of univalence and convexity involving generalized Bessel functions associated with the Hardy space and a monotonicity property of generalized and normalized Bessel functions of the first kind.

Original language | English |
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Title of host publication | Lecture Notes in Mathematics |

Publisher | Springer Verlag |

Pages | 23-69 |

Number of pages | 47 |

DOIs | |

Publication status | Published - Jan 1 2010 |

### Publication series

Name | Lecture Notes in Mathematics |
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Volume | 1994 |

ISSN (Print) | 0075-8434 |

ISSN (Electronic) | 1617-9692 |

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### Keywords

- Analytic Function
- Bessel Function
- Convex Function
- Geometric Property
- Unit Disk

### ASJC Scopus subject areas

- Algebra and Number Theory

### Cite this

*Lecture Notes in Mathematics*(pp. 23-69). (Lecture Notes in Mathematics; Vol. 1994). Springer Verlag. https://doi.org/10.1007/978-3-642-12230-9_2