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Fixed-point theorem for asymptotic contractions of Meir–Keeler type in complete metric spaces. (English) Zbl 1101.54047
Motivated essentially by the work of W. A. Kirk [J. Math. Anal. Appl. 277, No. 2, 645–650 (2003; Zbl 1022.47036)] and T.-C. Lim [Nonlinear Anal., Theory Methods Appl. 46, No. 1(A), 113–120 (2001; Zbl 1009.54044)], the author introduces the concept of asymptotic contraction of Meir-Keeler ($$ACMK$$) type on a metric space and obtains fixed point theorems fo such maps. The main result states that if $$T$$ is an $$ACMK$$ on a complete metric space $$X$$ and if $$T^l$$ is continuous for some natural number $$l$$, then $$T$$ has a unique fixed point.

##### MSC:
 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems
##### Citations:
Zbl 1022.47036; Zbl 1009.54044
Full Text:
##### References:
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