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(7 citation statements)

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“…The concept of a b-metric space was introduced by Czerwik in [11]. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric space [3,6,7,8,9,10,11,12,13,24,29].…”

confidence: 99%

“…The concept of a b-metric space was introduced by Czerwik in [11]. Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric space [3,6,7,8,9,10,11,12,13,24,29].…”

confidence: 99%

“…If b = 1, then b-metric space is a metric spaces. But the converse does not hold in general [3,9,11].…”

confidence: 99%

“…Note that there are fixed point theorems (see [7]) that cannot be transported from metric to b∽MSs as in the case of BCP.…”

confidence: 99%

“…A bifunction ρ: Z × Z ⟶ R + is a b ∼ metric on Z if there exists a κ ∈ R with κ ≥ 1 such that for u, y, z in Z, ρ satisfies (i) a 1 − ρ(u, y) � 0 if u � y (ii) a 2 − ρ(u, y) � ρ(y, u) (iii) a 3 − ρ(u, y) ≤ κρ(u, z) + κρ(z, y) e pair (Z, ρ) is known as b ∼ metric space (s) (shortly as b ∼ MS (s)) with b-metric constant κ. Clearly, for κ � 1, (Z, ρ) is a metric space, but there are b ∼ metrics that are not metrics (see [4,7,8]).…”

confidence: 99%

“…R + is said to be a b-metric if for any x; y; z 2 X; the following conditions hold: If b = 1; then b-metric space is a metric space. However, the converse does not hold in general ( compare [2,Example 3.9] and [8,9,20] ).…”

confidence: 99%