### Abstract

Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator.

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

Pages (from-to) | 17-28 |

Number of pages | 12 |

Journal | Integral Transforms and Special Functions |

Volume | 22 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2011 |

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### Keywords

- Analytic functions
- Bounded turning
- Cesàro means
- Close-to-convex functions
- Convex functions
- Dziok-srivastava linear operator
- Fox-wright hypergeometric function
- Fractional integral operator
- Fractional powers
- Generalized hypergeometric function
- Hadamard product (or convolution)
- Laplace transform
- Partial sums
- Subordination between analytic functions
- Univalent functions

### ASJC Scopus subject areas

- Applied Mathematics
- Analysis

### Cite this

*Integral Transforms and Special Functions*,

*22*(1), 17-28. https://doi.org/10.1080/10652469.2010.489796

**Classes of analytic functions with fractional powers defined by means of a certain linear operator.** / Srivastava, H. M.; Darus, Maslina; Ibrahim, Rabha W.

Research output: Contribution to journal › Article

*Integral Transforms and Special Functions*, vol. 22, no. 1, pp. 17-28. https://doi.org/10.1080/10652469.2010.489796

}

TY - JOUR

T1 - Classes of analytic functions with fractional powers defined by means of a certain linear operator

AU - Srivastava, H. M.

AU - Darus, Maslina

AU - Ibrahim, Rabha W.

PY - 2011/1

Y1 - 2011/1

N2 - Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator.

AB - Motivated by the success of the familiar Dziok-Srivastava convolution operator, we introduce here a closely-related linear operator for analytic functions with fractional powers. By means of this linear operator, we then define and investigate a class of analytic functions. Finally, we determine certain conditions under which the partial sums of the linear operator of bounded turning are also of bounded turning. We also illustrate an application of a fractional integral operator.

KW - Analytic functions

KW - Bounded turning

KW - Cesàro means

KW - Close-to-convex functions

KW - Convex functions

KW - Dziok-srivastava linear operator

KW - Fox-wright hypergeometric function

KW - Fractional integral operator

KW - Fractional powers

KW - Generalized hypergeometric function

KW - Hadamard product (or convolution)

KW - Laplace transform

KW - Partial sums

KW - Subordination between analytic functions

KW - Univalent functions

UR - http://www.scopus.com/inward/record.url?scp=78650271645&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=78650271645&partnerID=8YFLogxK

U2 - 10.1080/10652469.2010.489796

DO - 10.1080/10652469.2010.489796

M3 - Article

VL - 22

SP - 17

EP - 28

JO - Integral Transforms and Special Functions

JF - Integral Transforms and Special Functions

SN - 1065-2469

IS - 1

ER -