Aplicaciones no conmutativas y puntos fijos

 If f, g are continuous maps of a complete metric space X such that fg = gf, d(g(x),g(y) ∝d(f (x),f (y) for some 0 < ∝ < 1, and g(X) ⊑ f(X) ) ⊑ X, then f, g have a common fixed point. This is a result of G. Jungck; K.M. Das and K. Viswanatha Naik have generalized this ~esult by deleting the continuity of f but assuming instead that of ^f2. A result that generalizes those above, but does not assume thecontinuity of either f or f2 or the commutativity of f and g is proposed. The impossed conditions are that for some non empty complete subset K of X, g(K) ) ⊑ f(K) ~ K, that d(g(x), g(y)) ad(f(x),f(y)), 0 < ∝  < 1, x,y ∈ K, and that if x ∈ X, the existence of a sequence {x_n} of K such that lím f(x_n) = lím g(x_n) = x ensures that f(x) = g(x).