For analytic functions f (z) in the open unit disk E and convex functions g(z) in E, has proved one theorem which is a generalization of the result by K. Sakaguchi [K. Sakaguchi, On a certain univalent mapping, J. Math. Soc. Japan 11 (1959) 72–75]. The object of the present paper is to generalize the theorem due to Pommerenke.

An example of non-Markovian quantum dynamics is considered in the framework a geometrical (topological) subordination approach. The specific property model that it coincides exactly with fractional diffusion equation, which describes geometric Brownian motion on combs. Both classical and are described using dilatation operator xddx. Two examples subordinators considered. first one Gaussian func...

A new class of analytic functions of complex order is defined using a generalized differential operator. Coefficient inequalities, sufficient condition and an interesting subordination result are obtained.

Making use of the principle of differential subordination, we investigate some inclusion relationships of certain subclasses of multivalent analytic functions associated with the Wright generalized hypergeometric function.