On Jungck's common fixed point theorem

Abstract

Imdad and Javid proved an interesting generalization of Jungck’s common fixed point theorem for two commuting self-mappings of a complete metric space. However, their result require that the range of one of the mappings is a complete subspace of the metric space. In this paper, we use the (CLRg) property to obtain one which does not require the completeness of the range of the mappings involved therein. Our main result generalizes, in particular, single-valued versions of the classical common fixed point results of Kaneko and Sessa [ Internat. J. Math. & Math. Sci. 12 (2) (1989), 257 – 262 ] and Pathak [ Acta Math. Hungar 67 (1995), 69 – 78 ]. Also, we provide an example to distinguish our result from previously known results.