### Abstract

In this paper, we introduce and investigate two subclasses H_{β}^{*}(n, b,ϕ) and Kβ(n, b,ϕ) of analytic functions with negative coefficients of order β in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(α), and convex K(α) of order α respectively. We also obtain the same coefficient inequalities and distortion theorem for such univalent functions with negative coefficients. We point out that the coefficient estimates up to z^{9} are enough to get the graphs of starlike and convex functions. Here in the sequel we give some examples, estimation and the graphical representation of such univalent functions by using the complex tool [8].

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

Pages (from-to) | 509-515 |

Number of pages | 7 |

Journal | Applied Mathematics and Information Sciences |

Volume | 12 |

Issue number | 3 |

DOIs | |

Publication status | Published - 1 May 2018 |

### Fingerprint

### Keywords

- Convex functions
- Distortion theorems
- Starlike functions
- Univalent functions

### ASJC Scopus subject areas

- Analysis
- Numerical Analysis
- Computer Science Applications
- Computational Theory and Mathematics
- Applied Mathematics

### Cite this

*Applied Mathematics and Information Sciences*,

*12*(3), 509-515. https://doi.org/10.18576/amis/120305

**Graphing examples of starlike and convex functions of order β.** / Rehman, Hameed Ur; Darus, Maslina; Salah, Jamal.

Research output: Contribution to journal › Article

*Applied Mathematics and Information Sciences*, vol. 12, no. 3, pp. 509-515. https://doi.org/10.18576/amis/120305

}

TY - JOUR

T1 - Graphing examples of starlike and convex functions of order β

AU - Rehman, Hameed Ur

AU - Darus, Maslina

AU - Salah, Jamal

PY - 2018/5/1

Y1 - 2018/5/1

N2 - In this paper, we introduce and investigate two subclasses Hβ*(n, b,ϕ) and Kβ(n, b,ϕ) of analytic functions with negative coefficients of order β in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(α), and convex K(α) of order α respectively. We also obtain the same coefficient inequalities and distortion theorem for such univalent functions with negative coefficients. We point out that the coefficient estimates up to z9 are enough to get the graphs of starlike and convex functions. Here in the sequel we give some examples, estimation and the graphical representation of such univalent functions by using the complex tool [8].

AB - In this paper, we introduce and investigate two subclasses Hβ*(n, b,ϕ) and Kβ(n, b,ϕ) of analytic functions with negative coefficients of order β in the unit disk D. Silverman [6] determined certain coefficient inequalities and distortion theorems for univalent functions with negative coefficients that are starlike S(α), and convex K(α) of order α respectively. We also obtain the same coefficient inequalities and distortion theorem for such univalent functions with negative coefficients. We point out that the coefficient estimates up to z9 are enough to get the graphs of starlike and convex functions. Here in the sequel we give some examples, estimation and the graphical representation of such univalent functions by using the complex tool [8].

KW - Convex functions

KW - Distortion theorems

KW - Starlike functions

KW - Univalent functions

UR - http://www.scopus.com/inward/record.url?scp=85047069914&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85047069914&partnerID=8YFLogxK

U2 - 10.18576/amis/120305

DO - 10.18576/amis/120305

M3 - Article

VL - 12

SP - 509

EP - 515

JO - Applied Mathematics and Information Sciences

JF - Applied Mathematics and Information Sciences

SN - 1935-0090

IS - 3

ER -