ABSTRACT

The Lipschitz condition is of great importance in many branches of mathematics. The standard situation is the following: let (M,ρ) be a metric space; we say that a mapping T : M →M is lipschitzian if there exists a constant k such that, for all x, y ∈M , we have

ρ(Tx, Ty) ≤ kρ(x, y). The class of all mappings satisfying the Lipschitz condition with a constant k is denoted by L(k). The smallest constant k for which the above inequality holds is called the Lipschitz constant for T and is denoted by k(T ).