Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the conve...Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn（., qn）} when n → ∞ and convergence rate of Bn（f,q;x） when f ∈ C^n-1 [0, 1], q → ∞ are also presented.展开更多
In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing th...In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.展开更多
文摘Recently, q-Bernstein polynomials have been intensively investigated by a number of authors. Their results show that for q ≠ 1, q-Bernstein polynomials possess of many interesting properties. In this paper, the convergence rate for iterates of both q-Bernstein polynomials and their Boolean sum are estimated. Moreover, the saturation of {Bn（., qn）} when n → ∞ and convergence rate of Bn（f,q;x） when f ∈ C^n-1 [0, 1], q → ∞ are also presented.
基金supported by the National Science Foundation of China(11271161)
文摘In this paper, the complete moment convergence for L~p-mixingales are studied.Sufficient conditions are given for the complete moment convergence for the maximal partial sums of B-valued L~p-mixingales by utilizing the Rosenthal maximal type inequality for B-valued martingale difference sequence, which extend and improve the related known works in the literature.
