Abstract
We show that most contractive conditions of integral type given recently by many authors coincide with classical ones. This is done with the help of a geometric lemma on subsets of the quadrant [ 0 , ∞ ) 2 . In particular, we extend a recent result of Suzuki who observed that an integral version of the Banach contraction principle given by Branciari could be derived from a classical fixed point theorem of Meir and Keeler. Nevertheless, we also give a new contractive condition of integral type which is independent of classical ones since it does not force the nonexpansiveness of a mapping.
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