Pathak, H. K.; Cho, Y. J.; Kang, S. M. Remarks on R-weakly commuting mappings and common fixed point theorems. (English) Zbl 0878.54032 Bull. Korean Math. Soc. 34, No. 2, 247-257 (1997). 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) Cited in 5 ReviewsCited in 39 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems Keywords:common fixed point; weakly commuting mappings Citations:Zbl 0830.54031; Zbl 0613.54029; Zbl 0791.54059 PDFBibTeX XMLCite \textit{H. K. Pathak} et al., Bull. Korean Math. Soc. 34, No. 2, 247--257 (1997; Zbl 0878.54032)