On some cone metric common fixed point results (Q2898678)

Investigation of cone metric spaces goes back to papers published by several Russian authors in the mid-20th century. \textit{B. Rzepecki} [Publ. Inst. Math., Nouv. Sér. 28(42), 179--186 (1980; Zbl 0482.47029)] and \textit{S.-D. Lin} [Indian J. Pure Appl. Math. 18, 685--690 (1987; Zbl 0622.47057)] reintroduced such spaces calling them \(K\)-metric spaces. L.-G. Huang and X. Zhang studied such spaces, and also went further, defining convergent and Cauchy sequences in the terms of interior points of the underlying cone. \textit{H. Çakallı, A. Sönmez} and \textit{C. Genç} [Appl. Math. Lett. 25, No. 3, 429--433 (2012; Zbl 1245.54038)] proved that any cone metric space is metrizable. In the present paper under review the author proves that the common fixed point theorems presented in [\textit{F. Sabetghadam} and \textit{H. P. Masiha}, Fixed Point Theory Appl. 2010, Article ID 718340, 8 p. (2010; Zbl 1188.54023)] follow from an earlier result obtained by \textit{C. Di Bari} and \textit{P. Vetro} [ Rend. Circ. Mat. Palermo (2) 57, No. 2, 279--285 (2008; Zbl 1164.54031)] and \textit{G. Jungck, S. Radenovic, S. Radojevic} and \textit{V. Rakocevic} [Fixed Point Theory Appl. 2009, Article ID 643840, 13 p. (2009; Zbl 1190.54032)].