Application examples of the network fixed point theory for space-air-ground integrated communication network

The space-air-ground integrated network is based on the modern communication networks and integrated the latest communication and computer technologies, such that connects all various networks together to form a very huge and complicated network topology that has the best sharing of the global information and resources. This paper is treating the communication network as a space which is formed by the node iterative sequences of the path prediction algorithms. The fixed point theory could be widely used in such communication network space. It is making use of the mathematical reasoning method and through the operator based on some kind of router principle, such that the source node is mapping to the target node, and the target node is corresponding to the fixed point of the Banach space, that is the fixed point of the network space. Application examples of the network fixed point theory will be introduced in this paper and examples have shown that the fixed point theory is a favorable theoretical background for the network organization, dynamic characteristic and regularity of the space-air-ground integrated network.