Lois-Prados, CristinaRodríguez López, RosanaPrecup, Radu2024-01-112024-01-112020C. Lois-Prados, R. Precup, R. Rodríguez-López (2020). Krasnosel'skii type compression-expansion fixed point theorem for set contractions and star convex sets. Journal of Fixed Point Theory and Applications, 22(63).http://hdl.handle.net/10347/31804This is a post-peer-review, pre-copyedit version of an article published in Journal of Fixed Point Theory and Applications. The final authenticated version is available online at: http://dx.doi.org/10.1007/s11784-020-00799-0In 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internacionalhttp://creativecommons.org/licenses/by-nc-nd/4.0/compression-expansion fixed point theoremset contractionstar convex setimplicit differential system47H1034A09journal article10.1007/s11784-020-00799-01661-7746open access