## Abstract

Let consider A _{p} denoting a class of analytical functions defined as f(z)=z ^{p} +a _{p+1} z ^{p+1} +⋯+a _{p+n} z ^{p+n} +⋯ and p-valent in unit disc U={z||z|<1}. f(z)∈ A _{p} is expressed to be p-valently starlike in U if there is a positive figure ρ fulfilling ρ < |z| < 1, Re(z [Formula presented])>0, and ∫02πRe(z [Formula presented])dθ=2pπ, z=re ^{iθ} , ρ < r < 1. Let us consider S*(p)denoting the family of f(z)in A _{p} , being regular and p-valently starlike in U. It was proved by Goodman [3]that f(z)∈ S*(p)is at most p-valent in U. In present study, some results about radius of starlikeness of p-valent λ-fractional operator were obtained. Also some relevant corollaries were given. Finally, a result associated with p-valent λ-fractional operator by using convolution was given as a conclusion. The aim of this study is to give some results on λ-fractional operator of f(z)∈ S*(p).

Original language | English |
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Pages (from-to) | 374-378 |

Number of pages | 5 |

Journal | Applied Mathematics and Computation |

Volume | 357 |

DOIs | |

Publication status | Published - 15 Sept 2019 |

### Bibliographical note

Publisher Copyright:© 2018 Elsevier Inc.

### Funding

The work presented here is supported by Istanbul Technical University Scientific Research Project Coordination Unit. Project Number: TGA-2018-41339 .

Funders | Funder number |
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Istanbul Teknik Üniversitesi | TGA-2018-41339 |

## Keywords

- Convolution
- Fractional operator
- Radius of starlikeness