Classes with negative coefficients and starlike with respect to other points II

Abstract

A class $ S_{s}^{\star}T(\alpha,\beta,\sigma,k) $ of functions $ f $ which are analytic and univalent in the open unit disk $ {D=\{z:|z|<1\}} $ given by $ f(z)=z-{\sum_{n=2}^{\infty}}{a_n}{z^n} $ and satisfying the condition

$ \abs{\frac{zf'(z)}{f(z)-f(-z)}-k}<\beta \abs{\frac{\alpha zf'(z)}{f(z)-f(-z)}-(2\sigma-k)} $

for $ 0\leq \alpha \leq 1,0< \beta\leq1,0 \leq \sigma \leq \frac{1}{2}$ is introduced and studied. An analogous class $ S_{c}^{\star}T(\alpha,\beta,\sigma,k) $ and $ S_{sc}^{\star}T(\alpha,\beta,\sigma,k) $ are also examined.