Teorema de punto fijo común para funciones ocasionalmente débilmente compatibles satisfaciendo una condición contractiva con alteración de distancia

This paper aims to establish conditions that guarantee the existence and uniqueness of a common fixed point for a pair of functions defined on a metric space, satisfying a type of contractive inequality involving distance-altering functions. We use some weaker forms of commuting maps to achieve our results, concretely, occasionally weakly compatible maps. We prove that if f,g:(X,d)⟶(X,d)are occasionally weakly compatible maps with a coincident point such thatψ(d(g(x),g(y)))≤α(d(f(x),f(y)))∙ψ(d(f(x),f(y))),∀x,y∈Xwhere α:R+⟶[0,1)and ψis an altering distance function, then fand ghave a unique common fixed point. This result generalizes some theorems of common fixed points where neither the continuity of maps nor the completeness of the metricspace is required.