Wireless sensor networks with modular metric spaces

Chistyakov introduced notions of Metric Modular Spaces (MMS) recently. There are motivating chances when integrating the Fixed-Point Theorem (FPT) of MMS into the model and function of a Wireless Sensor Network (WSN), particularly when it comes to reformation network functions, routing algorithms, and data aggregation methods. In WSN data communication, security is a dynamic problem. Dynamic routing algorithms improve data security without requiring any added information by finding the shortest path for data transmission between two connected data packets. Applications requiring remote environmental condition monitoring are increasingly using WSN. Specifically, dense WSNs are evolving as a critical detecting stage for the Internet of Things (IoT). WSN can form the raw data, and to assure effective data transfer, a network model and effective node direction are required. Data aggregation is a method used by WSN to design a data fusion policy, and minimum data is transmitted inside the network. The study’s objective is the existence and uniqueness of FPT in MMS via integral type contraction. Also, the iteration of Fixed Points (FP) of Contracts in Settings in MMS was studied in this paper.