Inverse theorems for generalized Bernstein polynomials of two variables

May 2003 ABSTRACT This thesis consists of five chapters. First chapter is devoted to the introduction. In the second chapter, basic definitions, basic information on modules of continuity of two variable functions and Lipschitz function are given. In the third chapter of the thesis, approximation problems were examined continuous functions space in the two variables and theorem on this space are given. In the fourth chapter, generalized Bernstein polynomials of two variables are given, the uniform approximation of the/ function on unit square of these polynomials and their rate of converges were observed. In the fifth and last chapter, inverse theorems for generalized Bernstein polynomials of two variables are proved. Science Code : 403.03.01 KeyWords. Bernstein Polynomials, Modules of Continuity, Rate of Convergence, Uniformly convergence, Inverse Theorems, Lipschitz Class. Page number : 84 Adviser : Assoc.Prof. Dr. Ertasiî İBİKLİ