Weakly compatible mappings with respect to a generalized c-distance and common fixed point results

Abstract In this paper, we consider weakly compatible mappings with respect to a generalized -distance in cone -metric spaces and obtain new common fixed-point theorems. Our results provide a more general statement, since we need not to nor the continuity of mappings and nor the normality of cone. In particular, we refer to the results of M. Abbas and G. Jungck [Common fixed point results for non-commuting mappings without continuity in cone metric spaces, J. Math. Anal. Appl. 341 (2008) 416–420]. Some corollaries and examples are presented to support the main result proved herein.