The notion of Banach operator pair is used as a new class of noncommuting maps. The common fixed point theorems for Banach operator pair have been proved. The concept of g-nonexpansive, g-asymptotically nonexpansive, asymptotically regular, p-starshaped sets have been used. An attempt has been made to obtain the best approximation to the common fixed point of Banach operator pair.The concept of orbital continuity has been used to obtain the existence of common fixed points of Banach operator pair. Generalized contractive type condition for three mappings is defined and obtained some common...