## Abstract

In this paper, we give or improve compression-expansion results for set contractions in conical domains determined by balls or star convex sets. In the compression case, we use Potter’s idea of proof, while the expansion case is reduced to the compression one by means of a change of variable. Finally, to illustrate the theory, we give an application to the initial value problem for a system of implicit first order differential equations

## Authors

Cristina **Lois-Prados
**Universidade de Santiago de Compostela, Santiago de Compostela, Spain

Radu **Precup**

Babes-Bolyai University, Cluj-Napoca, Romania

Rosana **Rodríguez-López
**Universidade de Santiago de Compostela, Santiago de Compostela, Spain

** **

## Keywords

Compression-expansion fixed point theorem; set contraction; star convex set; implicit differential system

## Paper coordinates

C. Lois-Prados, R. Precup, R. Rodríguez-López, *Krasnosel’skii type compression-expansion fixed point theorem for set contractions and star convex sets*, J. Fixed Point Theory Appl. 22 (2020), 63, https://doi.org/10.1007/s11784-020-00799-0

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## About this paper

##### Journal

Journal of Fixed Point Theory and Applications

##### Publisher Name

Springer

##### Print ISSN

1661-7738

##### Online ISSN

1661-7746

google scholar link

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