turkmath.org

In computer-aided geometric design, it is important which basis functions are used if we want to preserve the shape of the curve or surface. Bernstein basis functions are used to construct classical Bezier curves since they have a simple structure to use. They have also received attention for their utility in the numerical solution of integral and integro-differential equations. A number of different operators have been introduced and different generalizations have been made on the basis of the linear and positive Bernstein operators produced by certain Bernstein basis functions. Today, studies are still carried out using these operators. In this talk, I will focus on new developments on some new Bernstein basis functions, new Bernstein-type operators, and their certain implementations.