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Exam (elaborations)
Answers To Kirk-Shahzad’s Questions On Strong B-Metric Spaces
KIRK-SHAHZAD’S
KIRK-SHAHZAD’S
In 1993, Czerwik [4] introduced the notion of a b-metric which is a generalization of a metric with a view of generalizing the Banach contraction map theorem. Definition 1.1 ([4]). Let X be a non-empty set and d : X × X −→ [0, +∞) be a function such that for all x, y, z ∈ X, (1) d(x, y) = 0 if and only if x = y. (2) d(x, y) = d(y, x). (3) d(x, z) ≤ 2[d(x, y) + d(y, z)]. Then d is called a b-metric on X and (X, d) is called a b-metric space. After that, in 1998, Czerwik [5] gen...
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