## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the Janowski convexity and starlikeness of the confluent hypergeometric function

#### Abstract

For $-1 \leq B < A \leq 1$, conditions on $A$, $B$, $a$, $c$ are determined that ensure the confluent hypergeometric function $\Phi(a;c;z)$ satisfies the subordination $\Phi(a; c; z) \prec (1+Az)/ (1+Bz)$. This gives rise to conditions for $(c/a)( \Phi(a; c; z)-1)$ to be close-to-convex, $\Phi(a; c; z)$ to be Janowski convex, and $z\Phi(a; c; z)$ to be Janowski starlike.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 22, Number 2 (2015), 227-250.

Dates
First available in Project Euclid: 28 May 2015

https://projecteuclid.org/euclid.bbms/1432840860

Digital Object Identifier
doi:10.36045/bbms/1432840860

Mathematical Reviews number (MathSciNet)
MR3351038

Zentralblatt MATH identifier
1317.30014

#### Citation

Ali, Rosihan M.; Mondal, Saiful R.; Ravichandran, V. On the Janowski convexity and starlikeness of the confluent hypergeometric function. Bull. Belg. Math. Soc. Simon Stevin 22 (2015), no. 2, 227--250. doi:10.36045/bbms/1432840860. https://projecteuclid.org/euclid.bbms/1432840860