DOI: 10.24193/fpt-ro.2022.1.15

Authors: J. Ferrer and E. Llorens-Fuster

Abstract: We give here a dichotomic fixed point result for a certain class of mappings defined in the closed unit ball of a Hilbert space. This dichotomy states that, for any of the mappings in this class, either it has a fixed point or its Lipschitz constant with respect to any renorming of 𝓁₂ has to be strictly greater than 1.

Key Words and Phrases: Fixed point, nonexpansive mapping, classical fixed point free mappings.

2010 Mathematics Subject Classification: 47H10, 54H25.

Published on-line: February 1st, 2022.

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