G1[x_, y_] := 1 + Cos[x + y]/2; 
    G2[x_, y_] := 2 + Sin[x + y]/3;
x0 = 0.5; y0 = 2. ; dif = 1; dif1 = 1; 
    cont = 1;
While[dif > 0.0001  &&  cont < 20,  x1 = G1[x0, y0]; 
      y1 = G2[x0, y0]; 
dif = 
        Sqrt[(x1 - x0)^2 + (y1 - y0)^2]; 
      Print[" x1=", x1, "   y1=", y1]; cont = cont + 1;  
      Print["dif=", dif, "  k=", dif/dif1] ; x0 = x1; y0 = y1; 
      dif1 = dif]