A Review article on some generalizations of Banach's contraction principle

Sujata Goyal
International Research Journal of Engineering and Technology   unpublished
Let (X,d) be a metric space. The well known Banach's Contraction Principle states that if T: X  X is a contraction on X(i.e.d (Tx,Ty)  c d (x,y) for some 0  c<1 and for all x,y in X) and (X,d) is complete then T has a fixed point in X (i.e. Tx = x for some x in X) In this paper , a number of extensions of Banach contraction principle have been discussed .