# Subordination and superordination results for Φ-like functions

T. N. Shanmugam, S. Sivasubramanian, Maslina Darus

Research output: Contribution to journalArticle

3 Citations (Scopus)

### Abstract

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.

Original language English 20 Journal of Inequalities in Pure and Applied Mathematics 8 1 Published - 2007

### Fingerprint

Subordination
Analytic function
Differential Superordination
Differential Subordination
Unit Disk
First-order
Sufficient Conditions

### Keywords

• Convolution
• Differential subordination
• Differential superordination
• Subordinant

### ASJC Scopus subject areas

• Mathematics(all)

### Cite this

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

In: Journal of Inequalities in Pure and Applied Mathematics, Vol. 8, No. 1, 20, 2007.

Research output: Contribution to journalArticle

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