### Meir-Keeler contractions of integral type are still Meir-Keeler contractions.

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In this paper, we prove that a mapping $T$ on a metric space is contractive with respect to a $\tau $-distance if and only if it is Kannan with respect to a $\tau $-distance.

In order to observe the condition of Kannan mappings more deeply, we prove a generalization of Kannan’s fixed point theorem.

We prove that every 3-generalized metric space is metrizable. We also show that for any ʋ with ʋ ≥ 4, not every ʋ-generalized metric space has a compatible symmetric topology.

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