Generalization of some extremal problems on non-overlapping domains with free poles

TL;DR

This paper extends extremal problems on non-overlapping domains to more general point systems, employing separating transformations and learning functions to achieve improved, more precise estimations considering angular parameters and coefficients.

Contribution

It generalizes extremal problems to broader systems of points and introduces refined methods for better estimations using separating transformations and learning functions.

Findings

Improved estimations considering angular parameters.

Enhanced bounds using separating transformations.

Detailed analysis of solutions with free poles.

Abstract

Although much research has been devoted to extremal problems on non-overlapping domains little is known about all solutions of this problems. We generalized some of this problems on the case of more general systems of points. It was solved using separating transformations and learning functions in detail. Methods used in the paper allowed to get improve and more exact estimations taking into account angular parameters, coefficients of displacement and controlable functionals.