How can connect iPhones, so that when a function is called on one iPhone, it calls functions on other iPhones through the web and can transfer parameters through the internet as well. Are there any other solutions rather than using a web host?
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If the device you want to talk to is physically within range, you can either use Bluetooth (GameKit API is very simple) or the more complex Bonjour Protocol for device discovery in the local network.
If your devices are physically not in range, you will most likely not be able to avoid some kind of server that has a (REST?) API which handles requests.