Work

A Unified Approach to Compression–Expansion Fixed Point Theorems for Operators Systems and Applications

Year: 2026

Type: article

Abstract: In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel’skiĭ’s theorem in cones. The cone-compression and cone-expansion type conditions are imposed in a component-wise manner. Unlike related results in the literature, the operators are allowed to be defined in the Cartesian product of conical regions delimited by nonconvex sets. Our approach, based on the fixed point index, ensures the existence of a coexistence fixed point–that is, one with nontrivial components. As a first application, we establish several localization results for systems of integral equations between strictly star-shaped sets defined by functionals. These results cannot be derived solely from previous studies dealing with operators in annular regions. A second application concerns nonlinear systems involving the $$\Phi $$ Φ -Laplacian.

Source: Results in Mathematics

DOI: 10.1007/s00025-026-02652-1

Authors: Laura Mª Fernández–Pardo, Jorge Rodríguez–López

Institution: Universidade de Santiago de Compostela

Language: English

Topic: Fixed Point Theorems Analysis

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,090