Let be a -metric space with parameter , in the sense of S. Czerwik [Acta Math. Inform. Univ. Ostrav. 1, 5–11 (1993; Zbl 0849.54036)]. Let and be two weakly compatible self-mappings of such that: (1) and satisfy property (E.A) of M. Aamri and D. El Moutawakil [J. Math. Anal. Appl. 270, No. 1, 181–188 (2002; Zbl 1008.54030)]; (2) ; and (3)
for all such that , where is continuous and satisfies: (a) is nondecreasing in variable and nonincreasing in variable ; (b) for all ; and (c) for all . The author proves that if or is a closed subspace of , then and have a unique common fixed point. If the -metric is weakly continuous (i.e., if implies for every sequence in and all ), then the same conclusion holds with weaker assumptions for the function .