## Taiwanese Journal of Mathematics

### ON FUNCTIONS STARLIKE WITH RESPECT TO SYMMETRIC AND CONJUGATE POINTS

#### Abstract

A class $S_s^\ast (\alpha ,\beta )$ of functions $f$, regular and univalent in $D = \{z: | z | \lt 1\}$ given by $f(z) = z+\sum\limits^\infty _{n=2} a_n z^n$ and satisfying the condition $$\left |\displaystyle\frac{zf'(z)}{f(z)-f(-z)}-1\right |\lt \beta\left|\displaystyle\frac{\alpha zf'(z)}{f(z)-f(-z)}+1\right |,$$ $z\in D, 0 \leq \alpha \leq 1, 0 \lt \beta \leq 1$ is introduced and studied. An analogous class $S_c^\ast (\alpha ,\beta )$ is also examined.

#### Article information

Source
Taiwanese J. Math., Volume 2, Number 1 (1998), 57-68.

Dates
First available in Project Euclid: 18 July 2017

https://projecteuclid.org/euclid.twjm/1500406894

Digital Object Identifier
doi:10.11650/twjm/1500406894

Mathematical Reviews number (MathSciNet)
MR1609472

Zentralblatt MATH identifier
0909.30009

#### Citation

Sudharsan, T. V.; Balasubrahmanyam, P.; Subramanian, K. G. ON FUNCTIONS STARLIKE WITH RESPECT TO SYMMETRIC AND CONJUGATE POINTS. Taiwanese J. Math. 2 (1998), no. 1, 57--68. doi:10.11650/twjm/1500406894. https://projecteuclid.org/euclid.twjm/1500406894