Classes of spirallike functions defined by the Dziok-Srivastava operator

Making use of the Dziok-Srivastava operator, we introduce two classes of analytic functions and investigate convolution properties, the necessary and sufficient condition, coefficient estimates and inclusion properties for these classes

Subordination Properties for Certain Analytic Functions

The purpose of the present paper is to derive a subordination result for functions in the class ∗(,,) of normalized analytic functions in the open unit disk . A number of interesting applications of the subordination result are also considered

Survey on filtrations (parametric embeddings) of infinitesimal generators

This work is devoted to the so-called filtration theory of semigroup generators in the unit disk. It should be noted that numerous filtrations studied to nowdays have been introduced for different purposes and considered from different points of view. So, our aim is to summarize the known facts, to present common and distinct properties of filtrations as well as to study some new filtrations with an emphasis on their connection with geometric function theory and the dynamic features of semigroups generated by elements of different filtration families. Among the dynamic properties, we mention the uniform convergence on the unit disk and the sectorial analytical extension of semigroups with respect to their parameter. We also solve the Fekete--Szeg\"o problem over various filtration classes, as well as over non-linear resolvents