Bernstein Operator With Multiple Baskakov Operator And Jacobi Right Approach

Bernstein-type operates and multivariate Baskakov operators with Jacobi weight are studied in this dissertation. This dissertation consists of four chapters.In chapter one, approximition background, history, meaning, and progress are stated, and we introduce the recent development of Bernstein and Baskakov opera-tors.In chapter two, using K-functional, a direct theorem and an inverse theorem of weighted approximation for Bernstein-type operators are obtained, and an equiv-alent characterization of weighted approximation of Bernstein operators is estab-lished.In chapter three, we prove the unboundness of multivariate Baskakov operators with the normal weight. Introducing new norms, the upper bound estimation of multivariate Baskakov operators is obtained by using of new modulus of smoothness with Jacobi weight and decomposition technique.In the last part, we summarize the main conclusions of the paper and propose the questions and works on Bernstein-type operators and multivariate Baskakov operators in the further research.