# Let \((X,d_x)\) and \((Y,d_Y)\) be arbitrary metric spaces. A mapping \(f:(X,d_x)\rightarrow (Y,d_Y)\) is called a strict contraction if

Let \((X,d_x)\) and \((Y,d_Y)\) be arbitrary metric spaces. A mapping \(f:(X,d_x)\rightarrow (Y,d_Y)\) is called a strict contraction if

—>> there exist a constant \(k\in[0,1)\) such that \(d_Y(f(x),f(y))\leq kd_X(x,y)\) for all \(x,y\in X\)

there exist a constant \(k\in[0,1)\) such that \(d_Y(x,y)\leq kd_Y(x,y)\) for all \(x,y\in X\)

there exist a variable \(k\in\mathbb{N}\) such that \(d_X(f(x),f(y))\geq kd(x,y)\) for all \(x,y\in X\)

there exist a constant \(k\in\mathbb{N})\) such that \(d_Y(x,y)geq kd_X(x,y)\) for all \(x,y\in X\)