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Remarks on some recent metrical common fixed point theorems

✍ Scribed by M. Imdad; Javid Ali; M. Tanveer

Publisher: Elsevier Science
Year: 2011
Tongue: English
Weight: 205 KB
Volume: 24
Category: Article
ISSN: 0893-9659
DOI: 10.1016/j.aml.2011.01.045

No coin nor oath required. For personal study only.

✦ Synopsis

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.

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