Krasnosel’skii type compression-expansion fixed point theorem for set contractions and star convex sets

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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