### Abstract

In this work, a new generalized derivative operator M
^{m}
_{α,β,λ}
is introduced. This operator obtained by using convolution (or Hadamard product) between the linear operator of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright
_{p}
Ψ
_{q}
function and generalized polylogarithm functions defined by (formula presented) where m ∈ N
^{0}
= {0, 1, 2, 3, …} and min{ Re (α), Re (β)} > 0. By making use of (formula presented) M
_{α,}
_{β,}
_{λ}
f(z),
^{m}
a class of analytic functions is introduced. The sharp upper bound for the nonlinear |a
_{2}
a
_{4}
− a
^{2}
_{3}
(also called the second Hankel functional) is obtained. Relevant connections of the results presented here with those given in
^{3}

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

Pages (from-to) | 453-459 |

Number of pages | 7 |

Journal | Journal of Mathematics and Computer Science |

Volume | 18 |

Issue number | 4 |

DOIs | |

Publication status | Published - 1 Jan 2018 |

### Fingerprint

### Keywords

- Hankel determinant
- Modified Mittag-Leffler function
- Polylogarithms functions

### ASJC Scopus subject areas

- Mathematics(all)
- Computational Mathematics
- Computer Science Applications
- Computational Mechanics

### Cite this

*Journal of Mathematics and Computer Science*,

*18*(4), 453-459. https://doi.org/10.22436/jmcs.018.04.06

**Second hankel determinant for a class defined by modified mittag-leffler with generalized polylogarithm functions.** / Pauzi, M. N.M.; Darus, Maslina; Siregar, S.

Research output: Contribution to journal › Article

*Journal of Mathematics and Computer Science*, vol. 18, no. 4, pp. 453-459. https://doi.org/10.22436/jmcs.018.04.06

}

TY - JOUR

T1 - Second hankel determinant for a class defined by modified mittag-leffler with generalized polylogarithm functions

AU - Pauzi, M. N.M.

AU - Darus, Maslina

AU - Siregar, S.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this work, a new generalized derivative operator M m α,β,λ is introduced. This operator obtained by using convolution (or Hadamard product) between the linear operator of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright p Ψ q function and generalized polylogarithm functions defined by (formula presented) where m ∈ N 0 = {0, 1, 2, 3, …} and min{ Re (α), Re (β)} > 0. By making use of (formula presented) M α, β, λ f(z), m a class of analytic functions is introduced. The sharp upper bound for the nonlinear |a 2 a 4 − a 2 3 (also called the second Hankel functional) is obtained. Relevant connections of the results presented here with those given in 3

AB - In this work, a new generalized derivative operator M m α,β,λ is introduced. This operator obtained by using convolution (or Hadamard product) between the linear operator of the generalized Mittag-Leffler function in terms of the extensively-investigated Fox-Wright p Ψ q function and generalized polylogarithm functions defined by (formula presented) where m ∈ N 0 = {0, 1, 2, 3, …} and min{ Re (α), Re (β)} > 0. By making use of (formula presented) M α, β, λ f(z), m a class of analytic functions is introduced. The sharp upper bound for the nonlinear |a 2 a 4 − a 2 3 (also called the second Hankel functional) is obtained. Relevant connections of the results presented here with those given in 3

KW - Hankel determinant

KW - Modified Mittag-Leffler function

KW - Polylogarithms functions

UR - http://www.scopus.com/inward/record.url?scp=85061792748&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85061792748&partnerID=8YFLogxK

U2 - 10.22436/jmcs.018.04.06

DO - 10.22436/jmcs.018.04.06

M3 - Article

AN - SCOPUS:85061792748

VL - 18

SP - 453

EP - 459

JO - Journal of Mathematics and Computer Science

JF - Journal of Mathematics and Computer Science

SN - 2008-949X

IS - 4

ER -