Mathematics (Jul 2020)

On a Class of Generalized Nonexpansive Mappings

  • Simeon Reich,
  • Alexander J. Zaslavski

DOI
https://doi.org/10.3390/math8071085
Journal volume & issue
Vol. 8, no. 7
p. 1085

Abstract

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 In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.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

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