Mean nonexpansive mappings are mean isometries if and only if they are isometries.

Monday, October 3, 2016 - 15:00
Thackeray 703
Speaker Information
University of Pittsburgh

Abstract or Additional Information

The notion of a mean nonexpansive mapping was introduced in 2007 by Goebel and Japon Pineda as a generalization of the class of nonexpansive mappings.  In this talk, we define the notion of a  mean isometry and prove that all mean isometries defined on metric spaces must be isometries in the usual sense.  This result gives a partial answer to a question posed by Goebel and Japon Pineda regarding  the existence of approximate fixed point sequences for mean nonexpansive mappings defined on subsets of Banach spaces. Further, we define a new class of functions, more general than the  mean nonexpansive mappings, and study some of their properties pertaining to fixed point theory. This is joint work with Professor Torrey Gallagher from Bucknell University.

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