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Let ( X, M, ⪯, ∗ ) be a preordered fuzzy quasi-metric space.
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Observe that if ( X, M, ⪯ t, ∗ ) is a preordered fuzzy metric space which is ⪯ t -complete, then ( X, M, ∗ ) is a complete fuzzy metric space in the usual sense (see e.g. [19]).
Let ( P, ≽ ) be a preordered set.
Let ( P, ≽ P ) be a preordered set.
Let ( X, d l, ⪯ ) be a preordered dislocated metric space.
Definition 2.3 Let ( X, ⪯ ) be a preordered set and d be a metric on X.
Let ( X, ⪯ ) be a preordered set, and let T : X → X be a mapping.
Lemma 3.3 Let ( S i, ≽ i ) be a preordered set for every i = 1, 2, …, n.
Let ( X, ≼ ) be a preordered set endowed with a G ∗ -metric G and T : X → X be a given mapping.
Let ( P, ≽ ) be a preordered set equipped with a topology τ (it is also a topological space).
Definition 2.6 Let ( X, ≽ X ) be a preordered set and let F : X → 2 X ∖ be a set-valued mapping.
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CEO of Professional Science Editing for Scientists @ prosciediting.com