Erratum to: Some new theorems of expanding mappings without continuity in cone metric spaces

Abstract

In this note we correct some errors that appeared in the article (Han and Xu in Fixed Point Theory Appl. 2013:3, 2013) by modifying some conditions in the main theorems and corresponding corollaries. MSC: 47H10; 54H25

A hybrid class of expansive-contractive mappings in cone b-metric spaces

“…[1,23,25] The most recent and perhaps most general theorems on expanding mappings in cone metric spaces were initially proposed by Han and Xu [8] who considered a pair of surjective expansion mappings. [27] was an erratum of the results in [8] and a valid generalization of the results of Aage and Salunke [1]. Even though the maps considered in [27] are not necessarily continuous, the coefficients a i in the expanding conditions are taken to be positive.…”

“…[27] was an erratum of the results in [8] and a valid generalization of the results of Aage and Salunke [1]. Even though the maps considered in [27] are not necessarily continuous, the coefficients a i in the expanding conditions are taken to be positive.…”

“…In this manuscript, the theorems in [27] are improved: the coefficients in the "expanding" inequalities are not constrained to be positive thus paving way to a more general class which can be, in a classical sense, contractive, expansive or neither. The number of the maps considered is extended to four with the surjectivity assumption removed, and the ambient space is generalized to cone b-metric spaces.…”

“…Theorem 2.1 of Xu et al[27]) Let (X, d) be a cone metric space. Suppose the mapping f : X → X is onto and such…”