Abstract.
We revisit a fixed point theorem for contractions established by Felix Browder in 1968. We show that many definitions of contractive mappings which appeared in the literature after 1968 turn out to be equivalent formulations or even particular cases of Browder’s definition. We also discuss the problem of the existence of approximate fixed points of continuous mappings; in particular, we settle it in the affirmative for Browder contractions. Finally, we recall three problems concerning Browder contractions which remain unsolved.
Similar content being viewed by others
Author information
Authors and Affiliations
Corresponding author
Additional information
With great respect for Professor Felix E. Browder
Rights and permissions
About this article
Cite this article
Jachymski, J. Around Browder’s fixed point theorem for contractions. J. fixed point theory appl. 5, 47–61 (2009). https://doi.org/10.1007/s11784-008-0094-1
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11784-008-0094-1