Certain properties of parabolic starlike and convex functions of order \(\rho\)
The authors have obtained the property that \(z{f'(z)\over f(z)}\) and \(1+ z{f''(z)\over f'(z)}\) lie inside a certain parabola, with the normalization \(f(0)= 0\), \(f'(0) =1\) in the unit disc \(D= \{z\mid| z|< 1\}\). On the other hand, some particular examples of a function having the required properties are given and these examples are invariant under the particular integral operators. There is also determined the radius of uniformly convexity and the radius of uniformly starlikeness for certain functions. So obtained results are correct.
scientific article; zbMATH DE number 2074209