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.