Godard  has proved that a metric space
M is 0-hyperbolic if and only if F(M), the Lipschitzfree space over M (see the definition in the next section), is isometric to a subspace of some [L.
12] studied complex valued metric space
and proved common fixed point theorems for two self-mappings satisfying a rational type inequality.
There have been a number of generalizations of metric spaces
such as vector valued metric spaces
, G-metric spaces
, pseudometric spaces, fuzzy metric spaces
, D-metric spaces
, cone metric spaces
, and modular metric spaces
rho]], we define a borel [sigma]-field in a metric space
Note that that each Caristi mapping on a complete metric space
has a fixed point.
Proposition 12 Let (X, d) be a metric space
, [absolute value of X] = n, and let (X, [[delta].
Lakshmikantham, Fixed point theorems in partially ordered metric spaces
and applications, Nonlinear Anal.
Jain, "Coupled coincidence and common fixed point theorems for set-valued and single-valued mappings in fuzzy metric space
," Journal of Fuzzy Set Valued Analysis, vol.
We recall that (C(I),d) is a complete metric space
Henceforth, (X, d) shall be an asymmetric metric space
Let X be a geodesic metric space
- that is, a metric space
where any two points x and y are the endpoints of a curve of length d(x, y).
1985): Let (X,d) be a complete metric space
and T: X [right arrow] X a contraction mapping with contraction factor c [member of] [0,1).
Likewise because in the Schwarzschild metric space
is curved a spatial velocity velocity [[upsilon].
5] generalized the Banach contraction principle by using two closed subsets of a complete metric space
infinity]]) is a metric space
of fuzzy functions from (-[infinity],0] to [E.