Question

Should one use under any circumstances getters-setters of a class within the class?

Answer 1

Getters setters are generally used from outside class from inside directly access the fields.
The main advantage/purpose is encapsulation of getter setters,

If your getters setters has some logical code then use it.

for example :

public void setValue(int val){
  if(val > 100)
    this.val = 0;
  else
    this.val = val;
  }

Also see

• why-use-getters-and-setters
• More on getters and setters