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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