RENARKS ON REWEAKLY COMMUTING MAPPONGS AND COMMON FIXED POINT THEOREMS

Abstract

It was the turning point in the point arena when the notion of weak commutativity was introduced by Sessa [9] as a sharper tool to obtain common fixed points of mappings. As a result, all the results on fixed point theorems for commuting mappings were easily transformed in the setting of the new notion of weak commutativity of mappings. It gives a new impetus to the studying of common fixed points of mappings satisfying some contractive type conditions and a number of interesting results have been found by various authors. A bulk of results were produced and it was the centre of vigorous research activity in Fixed Point Theory and its Application in various other Branches of Mathematical Sciences in last two decades. A major break through was done by Jungck [3] when he proclaimed the new notion what he called of mapping and its usefulness for obtaining common fixed points of mappings was shown by him. There-after a flood of common fixed point theorems was produced by various researchers by using the improved notion of compatibility of mappings. of compatibility of mappings.