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Metrical common fixed point theorems without completeness and closedness. (English) Zbl 1274.54124
Summary: In this article, we point out that some recent results proved in [G. V. R. Babu and G. N. Alemayehu, Appl. Math. Lett. 24, No. 6, 975–981 (2011; Zbl 1261.54033)] are corollaries of the main result of [J. Ali and M. Imdad, Sarajevo J. Math. 4(17), No. 2, 269–285 (2008; Zbl 1180.54052)]. However, combining the notions of R-weakly commuting property of type (Ag) (due to H. K. Pathak et al. [Bull. Korean Math. Soc. 34, No. 2, 247–257 (1997; Zbl 0878.54032)]) together with sequential continuity of type (Ag) (to be introduced in this note) (also, alternately, R-weakly commuting property of type (Af) (due to Pathak et al.) together with sequential continuity of type (Af) (to be introduced in this note)), these results are improved to yield possibly new results in metric fixed point theory.
54H25Fixed-point and coincidence theorems in topological spaces
54E40Special maps on metric spaces