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Fixed Point Principles for Cones of a Banach Space for the Multivalued Maps Differentiable at the Origin and Infinity

Published online by Cambridge University Press:  20 November 2018

Donald Violette  and
Gilles Fournier
Donald Violette
Affiliation:
Department de mathématiques, Université de Moncton, Monton, New Brunswick
Gilles Fournier
Affiliation:
Department de mathématiques, Université de Moncton, Monton, New Brunswick
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Abstract

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In [6] and [7], Krasnosel'skiĭ proved several fundamental fixed point principles for operators leaving invariant a cone in a Banach space. In [9], Nussbaum extended one of the results, the theorem about compression and expansion of a cone, to k-setcontraction maps, k < 1. Other versions for completely continuous maps were given by Fournier-Peitgen [2] and G. Fournier [1].

The purpose of this paper is to generalise some of these results to upper semi continuous multivalued maps which are K-set contractions, k < 1, and differentiable at the origin and infinity.

Keywords

47H0954C6054H25Fixed pointnonexpansive mappinginvariant meannonlinear ergodic theorem
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 44 , Issue 4 , 01 August 1992 , pp. 888 - 896
Copyright
Copyright © Canadian Mathematical Society 1992

References

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