## Remarks on some recent metrical common fixed point theorems.(English)Zbl 1296.54065

Summary: In an interesting article, H. Bouhadjera and 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.

### MSC:

 54H25 Fixed-point and coincidence theorems (topological aspects) 54E40 Special maps on metric spaces

Zbl 1231.54019
Full Text:

### References:

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