Contraction mapping on metric space

Question

We know the definition of contraction mapping. But it is unkown to me the definition of weak contraction mapping. Help me

Answer 1

A mapping $f:X\rightarrow X $ on a metric space is a $\bf{weak} $ contraction if for all $x\neq y\in X$ you have $$d(f(x),f(y))<d(x,y)$$ whereas a contraction is such a mapping where there is a constant $0<C<1$ so that $$d(f(x),f(y))\leq Cd(x,y)$$ for $\bf{all}$ $x,y\in X$. The answer I cited in the comment shows not every weak contraction is a contraction.