A generalization of strongly close-to-convex functions (Q2756090)

Let \(f(z)=z+\dots\) be a function analytic and locally univalent in the unit disc \(\mathbb{D}\), and let \(g(z)=z+\dots,z\in D\), belong to the Paatero class \(V_k\), \(2\leq k\leq 4\) of functions of bounded boundary rotation. The authors introduce a new class of functions defined as follows NEWLINE\[NEWLINEG_k(\beta)= \left\{f(z): \left|\text{arg}{f'(z)\over g'(z)}\right |\leq{\pi \beta \over 2},\;0\leq\beta <1,\;g\in V_k,\;z\in D\right\}.NEWLINE\]NEWLINE For \(f\) in \(G_k(\beta)\) they obtain distortion theorems, coefficient bounds and a covering theorem. Some of their results are sharp.