IN THIS PAPER, WE INTRODUCE THE NOTIONS OF OPERATOR (A, B, G) -MEAN, RELATIVE OPERATOR (A, B, G) -ENTROPY AND TSALLIS RELATIVE OPERATOR (A, B, G) -ENTROPY. WE GIVE UPPER AND LOWER BOUNDS OF RELATIVE OPERATOR (0, B, G) -ENTROPY AND TSALLIS RELATIVE OPERATOR (A, B, G) -ENTROPY WITH RESPECT TO OPERATOR (A, B, G) -MEAN.