1.1. Contraction operators. Let A be an operator defined on a set A in a Banach space E, satisfying a Lipschitz condition
1.1
$$\left\| {Ax - Ay} \right\| \le q\left\| {x - y} \right\|\left( {x,y \in \Re } \right).$$
If q < 1, A is called a contraction operator (or contracting operator).