Interpolative Contractive Results for $m$-Metric Spaces

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 \textquotedblleft interpolative exponents" is less than, equal to or greater than 1. We support each of our result 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 \cite{EY}, \cite{GH} and \cite{K} from ordinary metric to $m$- and $p$-metrics.