This article introduces the F-classes of the convex, starlike and close-to-convex classes of univalent functions. The paper also extends the theory of differential subordinations to F-differential subordinations and presents examples of these new concepts.

Differential equations of the form \(f'' + A(z)f' + B(z)f = 0\) (*) are considered, where A(z) and \(B(z) \not \equiv 0\) are entire functions. The Lindelöf function is used to show that for any \(\rho \in (1/2, \infty )\), there exists an equation of the form (*) which possesses a solution f with a Nevanlinna deficient value at 0 satisfying \(\rho =\rho (f)\ge \rho (A)\ge \rho (B)\), where \(\rho

The action of the Moisil-Theodoresco operator over a quaternionic valued function defined on \({\mathbb {R}}^3\) (sum of a scalar and a vector field) in Cartesian coordinates is generally well understood. However this is not the case for any orthogonal curvilinear coordinate system. This paper sheds some new light on the technical aspect of the subject. Moreover, we introduce a notion of quaternionic

For \(0