Abstract： The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the tes...Abstract： The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the test functions 1 and x2. This type of modification enables better error estimation on the interval[＋√3/3,＋∞] than the classic ones. Finally, a Voronovskaya-type theoremfor these operators is also obtained.展开更多
The purpose of this paper is to construct a multivariate generalization of a new kind of Kantorovich type q-Bernstein-Schurer operators. First, we establish the moments of the operators and then prove the rate of conv...The purpose of this paper is to construct a multivariate generalization of a new kind of Kantorovich type q-Bernstein-Schurer operators. First, we establish the moments of the operators and then prove the rate of convergence by using the modulus of continuity. Finally, we obtain the degree of approximation by means of Lipschitz type class.展开更多
文摘Abstract： The approximation operator for every kind of the objective function is different in approximation theory. For Lebesgue function, we introduce a kind of modified Kantorovich operators, which preserve the test functions 1 and x2. This type of modification enables better error estimation on the interval[＋√3/3,＋∞] than the classic ones. Finally, a Voronovskaya-type theoremfor these operators is also obtained.
文摘The purpose of this paper is to construct a multivariate generalization of a new kind of Kantorovich type q-Bernstein-Schurer operators. First, we establish the moments of the operators and then prove the rate of convergence by using the modulus of continuity. Finally, we obtain the degree of approximation by means of Lipschitz type class.
