Remarks on some recent metrical common fixed point theorems

https://doi.org/10.1016/j.aml.2011.01.045Get rights and content
Under an Elsevier user license
open archive

Abstract

In an interesting article, Bouhadjera and Godet-Thobie (2009) [6] introduced notions of subcompatibility and subsequential continuity, and utilized them to prove several common fixed point theorems. The results of the aforementioned article contain flaws, and they are not correct in their present form. But these results can be recovered in two ways by strengthening either of the newly introduced definitions. The results, in their corrected form, still bring about noted improvements over a multitude of relevant fixed point theorems of the existing literature, substantiating the utility of these (two) new notions.

Keywords

Compatible maps
Weakly compatible maps
Subcompatible maps
Subsequential continuity and reciprocal continuity

Cited by (0)