Interpolative contractive results for multivalued mappings over m-metric spaces with an application in homotopy

In this manuscript, we prove some new fixed point results for multivalued Kannan type interpolative contractive mappings over m-metric spaces. Our results cover all the possible cases of interpolative exponents: when their sum is equal to 1, less than 1 and greater than 1. We give examples to support our results. All the corresponding results in ordinary metric spaces are special cases of our new results for m-metric spaces. We also provide an application of homotopy to support our main result.