A unified approach to compression-expansion fixed point theorems for operators systems and applications
Fuente:
arXiv
Guardado en:
| Autores principales: | , |
|---|---|
| Formato: | Preprint |
| Publicado: |
2026
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866917297105403904 |
|---|---|
| author | Fernández-Pardo, Laura M. Rodríguez-López, Jorge |
| author_facet | Fernández-Pardo, Laura M. Rodríguez-López, Jorge |
| contents | In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii'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 Φ-Laplacian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_23243 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A unified approach to compression-expansion fixed point theorems for operators systems and applications Fernández-Pardo, Laura M. Rodríguez-López, Jorge Functional Analysis 47H10, 47H11, 45G15, 34B18 In this paper, we present some fixed point theorems for operator systems in the line of Krasnosel'skii'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 Φ-Laplacian. |
| title | A unified approach to compression-expansion fixed point theorems for operators systems and applications |
| topic | Functional Analysis 47H10, 47H11, 45G15, 34B18 |
| url | https://arxiv.org/abs/2602.23243 |