### Abstract

Let q_{1} be convex univalent and q_{2} be univalent in Δ := {z : |z| <1} with q_{1}(0) = q_{2} (0) = 1. Let f be a normalized analytic function in the open unit disk Δ. Let Φ be an analytic function in a domain containing f (δ) Φ(0) = 0 and Φ′(0) = 1. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for the function f to satisfy q_{1}(z)≺ z(f * g)′ (z)/Φ (f * g)(z) ≺ q_{2} (z) where g is a fixed function.

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

Article number | 20 |

Journal | Journal of Inequalities in Pure and Applied Mathematics |

Volume | 8 |

Issue number | 1 |

Publication status | Published - 2007 |

### Fingerprint

### Keywords

- Convolution
- Differential subordination
- Differential superordination
- Subordinant

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Journal of Inequalities in Pure and Applied Mathematics*,

*8*(1), [20].

**Subordination and superordination results for Φ-like functions.** / Shanmugam, T. N.; Sivasubramanian, S.; Darus, Maslina.

Research output: Contribution to journal › Article

*Journal of Inequalities in Pure and Applied Mathematics*, vol. 8, no. 1, 20.

}

TY - JOUR

T1 - Subordination and superordination results for Φ-like functions

AU - Shanmugam, T. N.

AU - Sivasubramanian, S.

AU - Darus, Maslina

PY - 2007

Y1 - 2007

N2 - Let q1 be convex univalent and q2 be univalent in Δ := {z : |z| <1} with q1(0) = q2 (0) = 1. Let f be a normalized analytic function in the open unit disk Δ. Let Φ be an analytic function in a domain containing f (δ) Φ(0) = 0 and Φ′(0) = 1. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for the function f to satisfy q1(z)≺ z(f * g)′ (z)/Φ (f * g)(z) ≺ q2 (z) where g is a fixed function.

AB - Let q1 be convex univalent and q2 be univalent in Δ := {z : |z| <1} with q1(0) = q2 (0) = 1. Let f be a normalized analytic function in the open unit disk Δ. Let Φ be an analytic function in a domain containing f (δ) Φ(0) = 0 and Φ′(0) = 1. We give some applications of first order differential subordination and superordination to obtain sufficient conditions for the function f to satisfy q1(z)≺ z(f * g)′ (z)/Φ (f * g)(z) ≺ q2 (z) where g is a fixed function.

KW - Convolution

KW - Differential subordination

KW - Differential superordination

KW - Subordinant

UR - http://www.scopus.com/inward/record.url?scp=34047183732&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34047183732&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:34047183732

VL - 8

JO - Journal of Inequalities in Pure and Applied Mathematics

JF - Journal of Inequalities in Pure and Applied Mathematics

SN - 1443-5756

IS - 1

M1 - 20

ER -