¿Restful Service opening socket connection and reuses the same connection in all requests?

I connect to a transactional server that is a Socket Server. As requirement are asked to have only one connection to the socket, and in this same connection all transactions are sent. I'm working with Java EE, Spring, Jboss server. The idea is to create a restful service, so other applications to connect and send transactions. Is it possible to open a client socket connection, and in the same connection open to send and receive messages client - server?

I have no idea how to do it, because every time you invoke the service rest, the application will attempt to create a new socket connection to the server, and will not reuse an already open connection.