### 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 |
---|---|

Volume | 1994 |

ISSN (Print) | 0075-8434 |

ISSN (Electronic) | 1617-9692 |

### Fingerprint

### 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

**Geometric Properties of Generalized Bessel Functions.** / Baricz, A.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

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

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TY - CHAP

T1 - Geometric Properties of Generalized Bessel Functions

AU - Baricz, A.

PY - 2010/1/1

Y1 - 2010/1/1

N2 - 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.

AB - 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.

KW - Analytic Function

KW - Bessel Function

KW - Convex Function

KW - Geometric Property

KW - Unit Disk

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U2 - 10.1007/978-3-642-12230-9_2

DO - 10.1007/978-3-642-12230-9_2

M3 - Chapter

AN - SCOPUS:85072867855

T3 - Lecture Notes in Mathematics

SP - 23

EP - 69

BT - Lecture Notes in Mathematics

PB - Springer Verlag

ER -