A Study on Fixed-Point Theory and Topological Structures Involving ϖb-Distance on θ-Complete Metric-Type Spaces

In this paper, we introduce a family of topologies τp on metric-type spaces (MTSs) using powers of the ϖb-distance. Moreover, we investigate fundamental topological properties, including convergence, closed sets, Cauchy sequences, and Hausdorffness, showing how varying p>0 affects these properties. Furthermore, we introduce some applications of ϖb-distance concerning the existence of fixed points (FPs) associated with generalized ϖbθ-contraction multivalued mappings given on MTSs, without imposing any completeness assumption. To support our main findings, we include several illustrative examples. In conclusion, our results either extend or enhance notable fixed-point theorems of metric FP theory.