Approximation of functions

Abstract

In this report, we review the different types of continuity of functions and relation between them. We also describe the convergence of sequence and series and various definitions related to approximation theory, which are important for the convergence point of view. We discuss the basic theme of approximating functions by polynomial functions. Then, we study some properties and convergence behaviour of the Bernstein polynomials. The B`ezier curve and its properties have also been introduced. Lastly, we obtain the B`ezier variant of the certain Genuine hybrid operators and discuss their approximation behaviour.