Generalized alpha-close-to-convex functions (Q1035176)

Summary: We define classes \(G_\beta(\alpha,k,\gamma)\) as follows: \(f\in G_\beta(\alpha,k,\gamma)\) if and only if, for \(z\in E=\{z\in\mathbb C: | z|<1\}\), \[ \left|\text{arg\,}\left(\frac{(1-\alpha^2z^2)f'(z)}{e^{-i\beta}\phi'(z)}\right)\right|\leq \frac{\gamma\pi}{2},\qquad 0<\gamma\leq 1,\; \alpha\in[0,1],\;\beta\in(-\pi/2,\pi/2), \] where \(\phi\) is a function of bounded boundary rotation. Coefficient estimates, an inclusion result, arclength problems, and some other properties of these classes are studied.