We prove two generalizations: the first to Das and Naik’s theorem for a pair of compatible maps without continuity; and the next as an extension of our first result to three self-maps on a metric space X without compatibility, under a stronger contraction type inequality and restricting the completeness of X to its subspace. The latter is a significant generalization of a recent result of Pant et al.
Abstract. An extended generalization of recent result of Kikina and Kikina (2011) has been established through the notions of weak compatibility and the property E.A., under an implicit-type relation and restricted orbital completeness of the space. The result of this paper also extends and generalizes that of Imdad and Ali (2007).
Let (X, d) be a G-metric space, f , a self-map on X and x0 ∈ X. Some misconceptions are brought about in findings of Mustafa et al [2], and a fixed point theorem for a Chatterjee-type G-contraction on a complete G-metric space is proved. More over, the unique fixed point p will be its contractive fixed point, in the sense that for each each x0 ∈ X, the f -iterates x0, f x0, ..., f n x0, ... converge to p.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.