# Compression-expansion fixed point theorem in two norms and applications

## Abstract

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.

## Authors

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

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

## Keywords

Positive solution; Integral equation; Fixed point theorem in cones

## Paper coordinates

D. O’Regan, R. Precup, Compression-expansion fixed point theorem in two norms and applications,  J. Math. Anal. Appl. 309 (2005), 383-391, https://doi.org/10.1016/j.jmaa.2005.01.043

## PDF

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##### Journal

Journal of Mathematical Analysis and Applications

Elsevier

##### Online ISSN

0022-247X

MR2154122, Zbl 1078.47017