Equivalent conditions for generalized contractions on (ordered) metric spaces

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Fixed point results under various contractive conditions in partial metric spaces (2013, background): “Sometimes an additional function ψ is introduced, but it was showed in [9] that its usage can be avoided.”
Matkowski's type theorems for generalized contractions on (ordered) partial metric spaces (2013, background): “In a recent paper [12], Jachymski showed the equivalence between several generalized contractions on (ordered) metric spaces.”
Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces (2014, background): “Checking the proof of Theorem 4 in [13], it turns out also that in this case (ordered b-metric space) we can replace ψ in (2.”
Some fixed point results for (α,β)-(ψ,Φ)-contractive mappings (2014, background): “So, from the result of Jachymski [47], the condition”
Common fixed-point results for nonlinear contractions in ordered partial metric spaces (2011, background): “There exist a vast literature concerning its various generalizations and extensions (see [1-45]).”
SOME RESULTS ON WEAKLY CONTRACTIVE MAPS (2012, unknown): “Let us mention also an important recent paper of Jachymski [12] who showed that some of the results involving two functions ϕ ∈ Φ and ψ ∈ Ψ can be reduced to the case of one function ϕ′ ∈ Φ.”