Every time you receive a text message, your iPhone tries to catch your attention with alerts. Unfortunately, it will keep reminding you (twice more) if you ignore the alert. If once is enough for you, you can turn off the repeat alerts. Here's how you do it:
- Open Settings> Messages.
- Slide the Repeat Alert to OFF. Note that this just turns off repeated alerts. You'll still get one alert for each incoming message. If you don't want to hear any sounds, turn the ringer switch on the side of your phone to the OFF position.