Some inequalities for starlike functions (Q793176)

For normalized starlike univalent functions in the unit disc we derive upper and lower estimates for certain differential expressions of nth order (including \(| zf'(z)/f(z)|\) for \(n=1)\) in terms of \(| f(z)|\). Our results generalize and (or improve) earlier ones by Twomey and Singh. The operators and methods applied come from the theory of the Peschl-Bauer differential equation.