On an affinity principle by Krasnoselskii

TL;DR

This paper presents an abstract formulation of Krasnoselskii's duality principle, showing that solutions to nonlinear functional equations via fixed points in Banach spaces imply shared topological properties of the involved operators.

Contribution

It introduces a new abstract formulation of Krasnoselskii's duality principle, linking solutions of nonlinear equations to topological properties of operators across Banach spaces.

Findings

Operators share topological properties under certain conditions.

Solutions can be obtained via fixed points in different Banach spaces.

The duality principle is extended in an abstract setting.

Abstract

An abstract formulation of a duality principle established by Krasnoselskii is presented. Under appropriate conditions, it shall be shown that, if the solutions of a nonlinear functional equation can be obtained by finding fixed points of certain operators in possibly different Banach spaces, then these operators share some topological properties.