Abstract

RIVAS, Orlin  and  BARRERA, Wilmer. Common fixed point theorem for occasionally weakly compatible maps satisfying a contractive condition with altering distance. Novasinergia [online]. 2022, vol.5, n.2, pp.23-32.  Epub July 05, 2022. ISSN 2631-2654.  https://doi.org/10.37135/ns.01.10.02.

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∈X where α: ℝ + ⟶[0,1) and ψ is an altering distance function, then f and g have 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 metric space is required.

Keywords : Common fixed point; commutativity; occasionally weakly compatible map; altering distance function; E.A. property.

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