Compression-expansion fixed point theorem in two norms and applications


In this paper we present a two-norms version of Krasnoselskii’s fixed point theorem in cones. The abstract result is then applied to prove the existence of positive \(L_p\)  solutions of Hammerstein integral equations with better integrability properties on the kernels.


Donal O’Regan
Department of Mathematics, National University of Ireland, Galway, Ireland

Radu Precup
Department of Mathematics Babes-Bolyai University, Cluj-Napoca, Romania


Positive solution; Integral equation; Fixed point theorem in cones

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D. O’Regan, R. Precup, Compression-expansion fixed point theorem in two norms and applications,  J. Math. Anal. Appl. 309 (2005), 383-391,


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Journal of Mathematical Analysis and Applications

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MR2154122, Zbl 1078.47017

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