## 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.

### Keywords:

Fixed point; Banach contraction; Kannan mappings

### Citations:

Zbl 0209.27104; Zbl 1145.54026
Full Text:

### 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
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