| In approximation theory,approximation by positive linear operators is a very classical problem.Many mathematicians have investigated it and concluded many valuable, significent results.This paper will go on to investigate the approximation by positive linear operators and it consists of four chapters.In the first part,some fundamental theorem, symbol, concept are introduced, including some valuable results on linear positive operators.In the second part,we study the iterative approximation of a new sequence of linear positive operators.A Voronovskaja type asymptotic formula and an estimate on error in terms of higher-order modulus of continuity for the operators are obtained ,which generalize the corresponding work of the reference.In the third part, we study the Korovkin theorem that introduces uniform convergence of positive linear operators. Let Ln be a sequence of positive linear operators on C2π,satisfying that Ln(ei) converge in C2π (not necessarily to ei),conditions that Ln is monotonicity-preserving and variation diminishing do not suffice to insure the convergence of (Ln(f)) for all f ∈ C2π,we obtain the Korovkin-type theorem and give quantitative results for approximation properties of the Jackson operators and Y.Matsuoka operators as an applications.In the fourth part, we investigate A-statistical convergence and rate of A-statistical convergence of positive linear operators .we study A-statistical convergence of positive linear operators and rate of A-statistical convergence mapping the weighted integrable space Lp(ω1) into Lp(ω2).Furthermore, the Korovkin theorem is studied for different weighted space and convergence. |
