To avoid dark rings around eyes, ends of lips and downside nose, apply olive oil and give a massage for 15 min. It can reduce the problem.
As for the dark area around the mouth, it is due to lack of iron in the body. Cut a lemon in half, take out the inside. Clean it out completely so you are left with only the skin of the lemon. Now apply soap or cleanser on the inner part of the lemon skin. Not the outside yellow part. Apply the cleanser or soap and rub it for a minute around your mouth and your entire face for a few seconds it will even out your skin tone. Results can be seen in three days. But this routine has to be continued.