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Remarks on R-weakly commuting mappings and common fixed point theorems. (English) Zbl 0878.54032

R. P. Pant [J. Math. Anal. Appl. 188, No. 2, 436-440 (1994; Zbl 0830.54031)] defines two selfmaps \(f\) and \(g\) of a metric space \((X, d)\) to be \(R\)-weakly commuting if \(d(fgx, gfx) \leq R \cdot d(fx, gx)\) for all \(x \in X\) and some real number \(R > 0\). Obviously \(f\) and \(g\) are also compatible in the sense of G. Jungck [Int. J. Math. Math. Sci. 9, 771-779 (1986; Zbl 0613.54029)]. Similar results appear in literature, see, e.g., the papers of G. Jungck, P. P. Murthy and Y. J. Cho [Math. Jap. 38, No. 2, 381-390 (1993; Zbl 0791.54059)].
Reviewer: S.Sessa (Napoli)

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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