## Meir-Keeler contractions of integral type are still Meir-Keeler contractions.(English)Zbl 1142.54019

The classical Banach principle has many generalizations, one which is the well known A. Meir-E. Keeler fixed point theorem [J. Math. Anal. Appl. 28, 326–329 (1969; Zbl 0194.44904)]. In this nice paper, the author shows that a fixed point theorem for contractions of integral type due to A. Branciari [Int. J. Math. Sci. 29, No. 9, 531–536 (2002; Zbl 0993.54040)] is a particular case of the Meir-Keeler fixed point theorem. Bearing in mind this fact, the author considers Meir-Keeler contractions of integral type and compares this class with other types of contraction mappings. In the last section the author proves the $$\tau$$-distance (see the author’s paper [J. Math. Anal. Appl. 253, No. 2, 440–458 (2001; Zbl 0983.54034)]) version of the previous results.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems

### Keywords:

Fixed point; Meir-Keeler contraction; $$\tau$$-distance

### Citations:

Zbl 0194.44904; Zbl 0993.54040; Zbl 0983.54034
Full Text:

### References:

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