Application of some fixed-point theorems in approximation theory

In this paper, we study some fixed point theorems in approximation theory. Fixed point theory initially emerged in the article demonstrating existence of solutions of differential equations .which appeared in the second quarter of the 18th century. Lateral on this technique was improved as a method of successive approximations which was extracted and abstracted as a fixed point theorem in the framework of complete normed space. It is stated that fixed point theory is initiated by Stefan Banach. Fixed point theorem have been used in many instances in approximation theory. Brosowski gave some application of fixed point theory for approximation.