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The comma before an index represents partial space differentiation and dot over a variable represents partial time derivative.
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A lot of fixed point theorems were investigated in partial spaces (see, e.g., [3 11] and references therein).
In this respect, cone metric spaces, fuzzy metric spaces, partial metric spaces, quasi-metric spaces and b-metric spaces can be given as the main examples.
Many authors generalized and extended the notion of metric spaces such as b-metric spaces, partial metric spaces, generalized metric spaces, complex-valued metric space etc.
Every quasi-partial space is a quasi-partial b-metric space.
These spaces, partial metric spaces, were first introduced by Matthews in 1994.
In 2012, based on the definition of cone metric spaces and partial metric spaces, Sonmez [16, 17] defined a partial cone metric space and proved some fixed point theorems for contractive type mappings in complete partial cone metric spaces.
It is clear that both weak partial metric space and quasi-partial metric space are a weak quasi-partial metric space, but the converse may not be true.
Every partial metric space is a metric-like space.
A partial KKM space is an abstract convex space satisfying the partial KKM principle.
It is clear that every partial metric space is a partial b-metric space with the coefficient s = 1 and every b-metric space is a partial b-metric space with the same coefficient and zero self-distance.
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