A Fixed Point Theorem for Decreasing Functions

Author： Herzog Gerd   Kunstmann Peer Chr.  

Publisher： Taylor & Francis Ltd

ISSN： 0163-0563

Source： Numerical Functional Analysis and Optimization, Vol.34, Iss.5, 2013-04, pp. : 530-538

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Abstract

Let E be a Banach spaces ordered by a cone K. We prove a fixed point theorem for Lipschitz continuous monotone decreasing functions f: K → K, which proves the existence of a unique fixed point in cases where the Lipschitz constant of f is bigger than 1. This fixed point theorem can be applied to Hammerstein integral equations in a quite natural way.

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