It appears to me that you have two issues here. One is that JFrame does not have a close method, which has been addressed in the other answers.
The other is that you're having trouble referencing your JFrame. Within actionPerformed, super refers to ActionListener. To refer to the JFrame instance there, use MyExtendedJFrame.super instead (you should also be able to use MyExtendedJFrame.this, as I see no reason why you'd want to override the behaviour of dispose or setVisible).