On a Class of Generalized Nonexpansive Mappings

Mathematics

AlexanderJ. Zaslavski¹  Simeon Reich¹ 

[1] Department of Mathematics, The Technion—Israel Institute of Technology, Haifa 32000, Israel;

关键词: banach space;    convex set;    fixed point;    Hilbert space;    nonexpansive mapping;   

DOI  :  10.3390/math8071085

来源: DOAJ

【 摘 要 】

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 In the definition of this notion the norm has been replaced by a general function satisfying certain conditions.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

【 授权许可】

Unknown