×

Some similarity between contractions and Kannan mappings. (English) Zbl 1162.54019

Kannan’s fixed point theorem [R. Kannan, Bull. Calcutta Math. Soc. 60, 71–76 (1968; Zbl 0209.27104)] is the first fixed point theorem which takes care of discontinuous maps as well. Following the idea used in generalizing the well known Banach contraction theorem by T. Suzuki [Proc. Am. Math. Soc. 136, No. 5, 1861–1869 (2008; Zbl 1145.54026)], the authors obtain two variants of Kannan’s theorem [loc. cit.]. Further, they show that the Kannan contraction constant used in the new set up is the best.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
54E40 Special maps on metric spaces
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
PDF BibTeX XML Cite
Full Text: DOI EuDML

References:

[2] doi:10.2307/2316437 · Zbl 0179.28203
[4] doi:10.2307/2033633 · Zbl 0163.17705
[7] doi:10.1016/j.na.2007.08.064 · Zbl 1152.54358
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.