Stability of geometric properties of convolutions of univalent functions (Q1902788)

For \(f(z)= z+ \sum^\infty_{k= 2} a_k z^k\) and \(g(z)= z+ \sum^\infty_{k= 2} b_k z^k\) holomorphic in the unit disk, the author uses the abbreviations: \[ (f* g)(z)= z+ \sum^\infty_{k= 2} a_k b_k z^k,\quad (f\otimes g)(z)= z+ \sum^\infty_{k= 2} (a_k b_k)/k z^k, \] \[ N_\delta(f)= \Biggl\{g\mid \sum^\infty_{k= 2} k|b_k- a_k|\leq \delta\Biggr\}. \] For sets \(N\) and \(M\) of such functions he defines \[ N * M= \{f* g\mid f\in N\text{ and } g\in M\},\quad N\otimes M= \{f\otimes g\mid f\in N\text{ and } g\in M\}, \] \[ N_\delta(M) = \bigcup_{f\in M} N_\delta(f). \] For several subclasses \(N\), \(M\) and \(P\) of the class of functions univalent in the unit disk, he determines \[ \sup\{\delta\mid N_\delta(M)* N_\delta(N)\subset P\}\quad\text{and}\quad \sup\{\delta\mid N_\delta(M)* N_\delta(N)\subset P\}. \]