Aplicaciones no conmutativas y puntos fijos
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Jungck theorems, metric space / Teoremas de Jungck, espacio metrico (es)Descargas
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 {xn} of K such that lím f(xn) = lím g(xn) = x ensures that f(x) = g(x).
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Derechos de autor 1987 Revista Colombiana de Matemáticas
Esta obra está bajo una licencia internacional Creative Commons Atribución 4.0.