How do you call a space with a function which is symmetric, non negative, positive definite and which satisfies a quasi-triangle inequality:

$d(x,z) \leq C( d(x,y)+d(y,z) )$

for all $x,y,z$ and some $C > 1$?

That is, it satisfies all the axioms of a metric space except for the triangle inequality, which is replaced by the one above.

Can anyone provide any reference on this spaces?

Thanks.

How do you call a space with a function which is symmetric, non negative, positive definite and which satisfies a quasi-triangle inequality:

$d(x,z) \leq C( d(x,y)+d(y,z) )$

for all $x,y,z$ and some $C > 1$?

That is, it satisfies all the axioms of a metric space except for the triangle inequality, which is replaced by the one above.

Can anyone provide any reference on these spaces?

Thanks.