### Abstract

Problem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Livingston. Approach: A new class of multivalent analytic functions in the open unit disk U was introduced. An application of this class was posed by using the fractional integral operator. The integral operator of multivalent functions was proposed and defined. The previous well known integral operator was mentioned. Results: Having the integral operator, a class was defined and coefficient bounds established by using standard method. These results reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained the coefficient bounds. Conclusion: Therefore, new operators could be obtained with some earlier results and standard methods. New classes were formed and new results of special cases were obtained.

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

Pages (from-to) | 271-275 |

Number of pages | 5 |

Journal | Journal of Mathematics and Statistics |

Volume | 6 |

Issue number | 3 |

Publication status | Published - 2010 |

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### Keywords

- Convex function
- Fractional integral operator
- Hadamard product
- Multiplier transformation
- Multivalent analytic function
- Starlike function

### ASJC Scopus subject areas

- Mathematics(all)
- Statistics and Probability

### Cite this

*Journal of Mathematics and Statistics*,

*6*(3), 271-275.

**On certain classes of multivalent analytic functions.** / Ibrahim, Rabha W.; Darus, Maslina.

Research output: Contribution to journal › Article

*Journal of Mathematics and Statistics*, vol. 6, no. 3, pp. 271-275.

}

TY - JOUR

T1 - On certain classes of multivalent analytic functions

AU - Ibrahim, Rabha W.

AU - Darus, Maslina

PY - 2010

Y1 - 2010

N2 - Problem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Livingston. Approach: A new class of multivalent analytic functions in the open unit disk U was introduced. An application of this class was posed by using the fractional integral operator. The integral operator of multivalent functions was proposed and defined. The previous well known integral operator was mentioned. Results: Having the integral operator, a class was defined and coefficient bounds established by using standard method. These results reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained the coefficient bounds. Conclusion: Therefore, new operators could be obtained with some earlier results and standard methods. New classes were formed and new results of special cases were obtained.

AB - Problem statement: By means of the Hadamard product (or convolution), new class of function of power order was formed. This class was motivated by many authors namely MacGregor, Umezawa, Darus and Ibrahim and many others. The class indeed extended in the form of integral operator due to the work of Bernardi, Libera and Livingston. Approach: A new class of multivalent analytic functions in the open unit disk U was introduced. An application of this class was posed by using the fractional integral operator. The integral operator of multivalent functions was proposed and defined. The previous well known integral operator was mentioned. Results: Having the integral operator, a class was defined and coefficient bounds established by using standard method. These results reduced to well-known results studied by various authors. The operator was then applied for fractional calculus and obtained the coefficient bounds. Conclusion: Therefore, new operators could be obtained with some earlier results and standard methods. New classes were formed and new results of special cases were obtained.

KW - Convex function

KW - Fractional integral operator

KW - Hadamard product

KW - Multiplier transformation

KW - Multivalent analytic function

KW - Starlike function

UR - http://www.scopus.com/inward/record.url?scp=77956811113&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77956811113&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:77956811113

VL - 6

SP - 271

EP - 275

JO - Journal of Mathematics and Statistics

JF - Journal of Mathematics and Statistics

SN - 1549-3644

IS - 3

ER -