### Abstract

Problem statement: We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to well-known results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.

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

Pages (from-to) | 77-87 |

Number of pages | 11 |

Journal | Journal of Mathematics and Statistics |

Volume | 5 |

Issue number | 1 |

DOIs | |

Publication status | Published - 2009 |

### Fingerprint

### Keywords

- Convex functions
- Convolution
- Prestarlike functions
- Starlike functions
- Subordinations

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

**On new bijective convolution operator acting for analytic functions.** / Al-Refai, Oqlah; Darus, Maslina.

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 5, no. 1, pp. 77-87. https://doi.org/10.3844/jms2.2009.77.87

}

TY - JOUR

T1 - On new bijective convolution operator acting for analytic functions

AU - Al-Refai, Oqlah

AU - Darus, Maslina

PY - 2009

Y1 - 2009

N2 - Problem statement: We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to well-known results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.

AB - Problem statement: We introduced a new bijective convolution linear operator defined on the class of normalized analytic functions. This operator was motivated by many researchers namely Srivastava, Owa, Ruscheweyh and many others. The operator was essential to obtain new classes of analytic functions. Approach: Simple technique of Ruscheweyh was used in our preliminary approach to create new bijective convolution linear operator. The preliminary concept of Hadamard products was mentioned and the concept of subordination was given to give sharp proofs for certain sufficient conditions of the linear operator aforementioned. In fact, the subordinating factor sequence was used to derive different types of subordination results. Results: Having the linear operator, subordination theorems were established by using standard concept of subordination. The results reduced to well-known results studied by various researchers. Coefficient bounds and inclusion properties, growth and closure theorems for some subclasses were also obtained. Conclusion: Therefore, many interesting results could be obtained and some applications could be gathered.

KW - Convex functions

KW - Convolution

KW - Prestarlike functions

KW - Starlike functions

KW - Subordinations

UR - http://www.scopus.com/inward/record.url?scp=65449150216&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=65449150216&partnerID=8YFLogxK

U2 - 10.3844/jms2.2009.77.87

DO - 10.3844/jms2.2009.77.87

M3 - Article

VL - 5

SP - 77

EP - 87

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 1

ER -