) = 0 and | w ( z )| < 1, and such that f ( z ) = g ( w ( z )). If g is univalent, then f ≺ g if and only if f (0) = g (0) and f (𝔻) ⊂ g (𝔻). The class of starlike functions consists of all those functions f ∈ 𝒜 such that the domain
References  Bello , R ., and Opoola , T . Upper bounds for fekete-szego functions and the second hankel determinant for a class of starlike functions . IOSR Journal of Mathematics 12 , 2 ( 2017 ), 34 – 39 .  Duren , P. L . Univalent
Analytic functions with bounded Mocanu variation generalize the concept of α-convexity in the unit disc. We introduce and
study certain classes of such functions. Inclusion results are obtained and a sharp radius problem is solved.
In this study, we investigate approximation properties and obtain Voronovskaja type results for complex modified Szász-Mirakjan operators. Also, we estimate the exact orders of approximation in compact disks and prove that the complex modified Szász-Mirakjan operators attached to an analytic function preserve the univalence, starlikeness, convexity and spirallikeness in the unit disk.
If a i .erential one-map between normed spaces is continuous on a star-like open set an is i .erentiable possibly except of one point then it has a primitive if an only if its erivative as a bilinear form is symmetric at every point where it exists.A generalization of the theorem on the existence of the potential operator is also obtained.The proof is based on the idea of the Goursat Lemma.