In this paper, we initiate the study of fixed points for interpolative mappings in m-metric spaces. We discuss three different cases: the sum of “interpolative exponents” is less than, equal to, or greater than 1. We support each of our results by examples in m-metric spaces. In the last section, we obtain our results in p-metric spaces. Finally, we note that our results generalize results of [3], [4], and [5] from ordinary metric to m– and p-metrics.