descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 03 Jul 2020 English Publisher:MDPI AGJournal:Mathematics, volume 8, page 1,085 (eissn: 2227-7390,

Authors: Reich, Simeon; Zaslavski, Alexander J.;

doi: 10.3390/math8071085

On a Class of Generalized Nonexpansive Mappings

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Abstract

In our recent work we have introduced and studied a notion of a generalized nonexpansive mapping. In the definition of this notion the norm has been replaced by a general function satisfying certain conditions. For this new class of mappings, we have established the existence of unique fixed points and the convergence of iterates. In the present paper we construct an example of a generalized nonexpansive self-mapping of a bounded, closed and convex set in a Hilbert space, which is not nonexpansive in the classical sense.

Related Organizations

Technion – Israel Institute of Technology
Israel

Keywords

convex set, fixed point, Hilbert space, QA1-939, nonexpansive mapping, banach space, Mathematics

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