The Fekete–Szegö functional and filtration of generators

Abstract

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-Szegö problem over various filtration classes, as well as over non-linear resolvents.

On Inequalities and Filtration Associated with the Nonlinear Fractional Operator

“…For more details, see [12][13][14][15]. Moreover, we obtain the following result, as shown by Elin, see [9].…”

“…As a special case, if we take α = 0, µ = 1 and β ∈ R, we obtain the following corollary, as seen in [9]. Corollary 5.…”