### Abstract

Let S(α,β,λ) denote the class of analytic functions f defined on the unit disk D with the normalization f(0)=f^{'}(0)-1=0, z/f(z)≠0 in D and satisfy the condition {pipe}f'(z)(zf(z))2-βz3(zf(z))‴-(α+β)z2(zf(z))″-1{pipe}≤λ for all z∈D and for some real constants α>-1 and β such that α+β>-1. We find conditions on constants α>-1 and β such that functions in S(α,β,λ) are univalent in D. As a consequence of our investigation, we present univalence and starlikeness criteria. As applications, we present conditions such that z/u_{p,b,c} is in S(α,β,λ), where u_{p,b,c} denotes the suitably normalized form of the generalized Bessel functions of the first kind.

Original language | English |
---|---|

Pages (from-to) | 558-567 |

Number of pages | 10 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 400 |

Issue number | 2 |

DOIs | |

Publication status | Published - Apr 15 2013 |

### Fingerprint

### Keywords

- Analytic, univalent and starlike functions
- Bessel functions
- Coefficient inequality

### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

*Journal of Mathematical Analysis and Applications*,

*400*(2), 558-567. https://doi.org/10.1016/j.jmaa.2012.11.050

**Differential inequalities and Bessel functions.** / Baricz, A.; Ponnusamy, Saminathan.

Research output: Contribution to journal › Article

*Journal of Mathematical Analysis and Applications*, vol. 400, no. 2, pp. 558-567. https://doi.org/10.1016/j.jmaa.2012.11.050

}

TY - JOUR

T1 - Differential inequalities and Bessel functions

AU - Baricz, A.

AU - Ponnusamy, Saminathan

PY - 2013/4/15

Y1 - 2013/4/15

N2 - Let S(α,β,λ) denote the class of analytic functions f defined on the unit disk D with the normalization f(0)=f'(0)-1=0, z/f(z)≠0 in D and satisfy the condition {pipe}f'(z)(zf(z))2-βz3(zf(z))‴-(α+β)z2(zf(z))″-1{pipe}≤λ for all z∈D and for some real constants α>-1 and β such that α+β>-1. We find conditions on constants α>-1 and β such that functions in S(α,β,λ) are univalent in D. As a consequence of our investigation, we present univalence and starlikeness criteria. As applications, we present conditions such that z/up,b,c is in S(α,β,λ), where up,b,c denotes the suitably normalized form of the generalized Bessel functions of the first kind.

AB - Let S(α,β,λ) denote the class of analytic functions f defined on the unit disk D with the normalization f(0)=f'(0)-1=0, z/f(z)≠0 in D and satisfy the condition {pipe}f'(z)(zf(z))2-βz3(zf(z))‴-(α+β)z2(zf(z))″-1{pipe}≤λ for all z∈D and for some real constants α>-1 and β such that α+β>-1. We find conditions on constants α>-1 and β such that functions in S(α,β,λ) are univalent in D. As a consequence of our investigation, we present univalence and starlikeness criteria. As applications, we present conditions such that z/up,b,c is in S(α,β,λ), where up,b,c denotes the suitably normalized form of the generalized Bessel functions of the first kind.

KW - Analytic, univalent and starlike functions

KW - Bessel functions

KW - Coefficient inequality

UR - http://www.scopus.com/inward/record.url?scp=84872016390&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84872016390&partnerID=8YFLogxK

U2 - 10.1016/j.jmaa.2012.11.050

DO - 10.1016/j.jmaa.2012.11.050

M3 - Article

VL - 400

SP - 558

EP - 567

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -