Apporoximation properties of triangle bernstein polynomials in region [-1,1]x[-1,1]

In the present study, we considered Bernstein polynomials in the symmetric interval studied by Cilo (2012)., Stancu's (1968) Bernstein polynomials in the triangular region for functions of two variables to Cilo's work. In approximation theory, Berstein polynomials have been studied extensively for functions of one and more variables. Many generalizations and modifications of the linear positive operators defined in approximation theory have been made. Probably the most important of these is the Bernstein polynomials.. They have also been studied in quadratic and triangular regions for functions of two variables. We studied the approximation, the rate of approximation by using complete modulus ,continuty and partial modulus of continuity and the Voronovskaja-type asymptotic theorem (formula) are studied for these operators.. Also, graphical representations are added to demonstrate the consistency of theoretical findings for our operators approximating functions on the triangular domain by using Maple software. We aimed to apply Stancu's (1968) study of Bernstein polynomials in the triangular region for functions of two variables to Cilo's thesis. We studied the approximation, the rate of approximation and the Voronovskaya type approximation.