Fixed-point theory plays an important role in solving the existence and uniqueness of solutions of differential equation, in solving Eigen value Problems and Boundary Value problems. Fixed-point theory also contributes in characterization of the completeness of matric spaces. Due to its applications in various disciplines of mathematical sciences, the Banach contraction and fixed-point theorems have been established. The ideas have a much wider scope than might be suspected and can be applied to establish many other existence theorem in the theory of differential and integral equations. There arenumerous extension of Banach’s fixed point theorem by generalization its hypothesis while retaining the convergence property of successive iterations the unique fixed point of mapping.Inthepresent paper we discuss about fixed point and Nielsen fixed point theorems with some review Key words: fixed point, Nielsen fixed poin
