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Remarks on some recent metrical common fixed point theorems. (English) Zbl 1296.54065
Summary: In an interesting article, {\it H. Bouhadjera} and {\it C. Godet-Thobie} [Acta Math. Vietnam. 36, No. 1, 1--17 (2011; Zbl 1231.54019)] 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.

54H25Fixed-point and coincidence theorems in topological spaces
54E40Special maps on metric spaces
Full Text: DOI
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