Fixed point theorems in metric spaces and applications

The main object of this thesis is to study the fixed point theorems under contraction and contractive mappings in metric spaces. -- We have discussed the Banach's contraction principle, "A contraction mapping of a complete metric space into itself has a unique fixed point", together with its various generalizations in metric spaces. -- A few new results which guarantee the existence and uniqueness of fixed points for contraction, contractive mappings and mappings with a contractive iterate have been given for metric spaces. -- An attempt has been made to give more general theorems for mappings of the form d(Tx,Ty) ≤ ψ(d(x,y)) on metric spaces. A few fixed point theorems on generalized metric space have been obtained. -- In the end, some applications of the fixed point theorems are illustrated by taking suitable examples.