\(M_b^\ast\)-metric space and its applications. (English) Zbl 1498.54089
Summary: We extend the \(b\)-metric space to an \(M_b^\ast\)-metric space and also we study the topology of this new space. The results are illustrated by sufficient examples that guarantee that the results are real generalizations. We also prove some fixed point theorems in such metric spaces such as the Banach contraction principle. Moreover, an application in finding a unique solution for an integral equation is studied.
MSC:
54H25 | Fixed-point and coincidence theorems (topological aspects) |
54E40 | Special maps on metric spaces |