A pair ( f, g ) of self-mappings defined on a metric space ( X, d ) is said to be (i) compatible [9] iff lim n d ( f g x n, g f x n ) = 0 whenever { x n } is a sequence in X such that lim n f x n = lim n g x n = t for some t in X.
Definition 2.45 Two self-mappings f and g of a metric space ( X, d ) are called: (i) compatible of type ( P ) (Pathak et al. [47, 84, 85]) iff lim n d ( f f x n, g g x n ) = 0, (ii) compatible of type ( C ) (Singh [58]) iff lim n d ( f f x n, g g x n ) = 0 and lim n d ( f g x n, g f x n ) = 0, .
Mappings f, g : X → X are called (i) compatible if, whenever a sequence { x n } in X is such that { f x n } and { g x n } are convergent to some t ∈ X, then lim n → ∞ p ( f g x n, g f x n ) = p ( t, t ), and (ii) noncompatible if there exists at least one sequence { x n } in X such that { f x n } and { g x n } are convergent to some t ∈ X, but lim n → ∞ p ( f g x n, g f x n ) does not exist.
Definition 2.18 Two self-mappings f and g of a metric space ( X, d ) are called: (i) compatible of type ( A ) (Jungck et al. [34]) iff lim n d ( f f x n, g f x n ) = 0 and lim n d ( f g x n, g g x n ) = 0, (ii) compatible of type ( B ) (Pathak et al. [46]) iff lim n d ( f g x n, g g x n ) ≤ 1 2 [ lim n d ( f g x n, f t ) + lim n d ( f t, f f x n ) ] .
Diagnosis should be based on three criteria: (i) compatible clinical presentation, (ii) evidence of non-caseating epithelioid-cell granulomas, and (iii) exclusion of alternative granulomatous disorders [ 12].
A 360 bp PCR product containing XbaI/MfeI compatible ends and a unique HpaI restriction site was ligated into XbaI/MfeI-digested pZErO-2E3-2.7 pZErO-2E3-2.7 pZErO-2E3-2.72E3Δ19k-HpaI.
Is compatible with Tinder, Grindr, OkCupid, Match.com, and whatever dating app they invent next.
(v) Is compatible with the requirements of 29 U.S.C. 794(d), Section 508 of the Rehabilitation Act.
Is it compatible with being Scottish?
Is it compatible with being European?
Is it compatible with your values, interests or ambitions?
