In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previou...In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.展开更多
In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem c...In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.展开更多
In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.
In this paper, we show the direct and converse theorems of strong type of approximation for modified Szasz operators. Rom these theorems, the characterization of approximation for these operators is derived. The obtai...In this paper, we show the direct and converse theorems of strong type of approximation for modified Szasz operators. Rom these theorems, the characterization of approximation for these operators is derived. The obtained results are similar to the corresponding ones of the Szasz operators.展开更多
Abstract The rate of convergence for the Gamma operators cannot be faster than $$O{\left( {\frac{1}{n}} \right)}$$. In order to obtain much faster convergence, quasi-interpolants in the sense of Sablonnière are c...Abstract The rate of convergence for the Gamma operators cannot be faster than $$O{\left( {\frac{1}{n}} \right)}$$. In order to obtain much faster convergence, quasi-interpolants in the sense of Sablonnière are considered. For the first time in the theory of quasi-interpolants, the strong converse inequality is solved in sup-norm with the K-functional $$K^{\alpha }_{\lambda } {\left( {f,t^{{2r}} } \right)}\;{\left( {0 \leqslant \lambda \leqslant 1,\;0展开更多
In this paper, we obtain the strong converse inequality for Száisz operators with K-functional by introducing a new K-functional of the formKλ^α（f,t^2） =inf g∈Cλ^2{‖f -g‖o ＋t^2‖g‖2} （0 ≤ λ≤ 1,0 ≤...In this paper, we obtain the strong converse inequality for Száisz operators with K-functional by introducing a new K-functional of the formKλ^α（f,t^2） =inf g∈Cλ^2{‖f -g‖o ＋t^2‖g‖2} （0 ≤ λ≤ 1,0 ≤α ≤ 2）,where ‖· ‖o, ‖· ‖2,Cλ^2 are defined in the paper. As for its applications, we have extended some results before this paper.展开更多
基金the Foundation of Higher School of Ningxia(04M33)the NSF of Ningxia University(ZR0622)
文摘In this paper, we give the strong converse inequalities of type B with the new K-functional Kλα(f,t2)w(0 ≤λ≤ 1, 0 < α < 2) on weighted approximation for Sz′asz-Mirakjan operators, which extend the previous results.
基金Supported by National Science Foundation of China（10571040）
文摘In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2(0 < α < 2,0 ≤λ≤ 1) for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.
基金The NSF (10571040) of ChinaNSF (L2010Z02) of Hebei Normal University
文摘In this paper we give a strong converse inequality of type B in terms of unified K-functional Kλα （f, t2） （0 ≤λ≤ 1, 0 〈 α 〈 2） for the Meyer-Knig and Zeller-Durrmeyer type operators.
基金Supported by the Foundation of Key Item of Science and Technology of Education Ministry of China(03142)Foundation of Higher School of Ningxia(JY2002107)
文摘In this paper, we show the direct and converse theorems of strong type of approximation for modified Szasz operators. Rom these theorems, the characterization of approximation for these operators is derived. The obtained results are similar to the corresponding ones of the Szasz operators.
基金Supported by the Hebei Provincial Science Foundation of China (A2004000137)Doctoral Research Fund of Hebei Normal University (L2002B03)
文摘Abstract The rate of convergence for the Gamma operators cannot be faster than $$O{\left( {\frac{1}{n}} \right)}$$. In order to obtain much faster convergence, quasi-interpolants in the sense of Sablonnière are considered. For the first time in the theory of quasi-interpolants, the strong converse inequality is solved in sup-norm with the K-functional $$K^{\alpha }_{\lambda } {\left( {f,t^{{2r}} } \right)}\;{\left( {0 \leqslant \lambda \leqslant 1,\;0
基金the National Natural Science Foundation of China （No. 10571040） the Natural Science Foundation of Hebei Province （No. A2004000137）+1 种基金 the Doctorial Fund of Education Department of Hebei Province （No. B2004118） the Doctorial Fund of Hebei Normal University （No. L2003B04）.
文摘In this paper, we obtain the strong converse inequality for Száisz operators with K-functional by introducing a new K-functional of the formKλ^α（f,t^2） =inf g∈Cλ^2{‖f -g‖o ＋t^2‖g‖2} （0 ≤ λ≤ 1,0 ≤α ≤ 2）,where ‖· ‖o, ‖· ‖2,Cλ^2 are defined in the paper. As for its applications, we have extended some results before this paper.
