On a Class of Generalized Nonexpansive Mappings

Simeon Reich and Alexander J. Zaslavski
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Simeon Reich: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel
Alexander J. Zaslavski: Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel

Mathematics, 2020, vol. 8, issue 7, 1-8

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 In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.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.

Keywords: banach space; convex set; fixed point; Hilbert space; nonexpansive mapping (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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