In this paper, we derive the complete asymptotic expansion of classical Baskakov operators Vn （f;x） in the form of all coefficients of n^-k, k = 0, 1... being calculated explic- itly in terms of Stirling number of t...In this paper, we derive the complete asymptotic expansion of classical Baskakov operators Vn （f;x） in the form of all coefficients of n^-k, k = 0, 1... being calculated explic- itly in terms of Stirling number of the first and second kind and another number G（i, p）. As a corollary, we also get the Voronovskaja-type result for the operators.展开更多
There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.
In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
In this paper we obtain all other local Nikolskii constants for Baskakov operators by ap- plying a method of asymptotic expansions,give a complete and satisfactory solution of Lehnhoff s open problems[1].
In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give so...In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators.展开更多
In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Ba...In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Baskakov operators.展开更多
The Meyer-König and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation i...The Meyer-König and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation is extended to complex space;the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-König and Zeller operators were obtained.展开更多
In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
基金Supported by the Natural Science Foundation of Beijing(1072006)
文摘In this paper, we derive the complete asymptotic expansion of classical Baskakov operators Vn （f;x） in the form of all coefficients of n^-k, k = 0, 1... being calculated explic- itly in terms of Stirling number of the first and second kind and another number G（i, p）. As a corollary, we also get the Voronovskaja-type result for the operators.
文摘There are some equivalence theorems on Baskakov Operators. In this paper, we make use of ω 2 φ λ (f;t) to give a new equivalence theorem which includes the existing results as its special cases.
基金This research is supported by Zhejiang Provincial Natural Science Foundation of China.
文摘In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
文摘In this paper we obtain all other local Nikolskii constants for Baskakov operators by ap- plying a method of asymptotic expansions,give a complete and satisfactory solution of Lehnhoff s open problems[1].
基金This research is supported by the National Natural Science Foundation of Chinathe Zhejiang Provincial Natural ScienCe Foundation of China
文摘In this paper, we investigate the relation between the rate of convergence for the derivatives of the combinations of Baskakov operators and the smoothness for the derivatives of the functions approximated. We give some direct and inverse results on pointwise simultaneous approximation by the combinations of Baskakov operators. We also give a new equivalent result on pointwise approximation by these operators.
基金Research supported by Council of ScientificIndustrial Research, India under award no.9/143(163)/91-EMR-1.
文摘In the present paper, we define a new kind of positive linear operators and study the rate of convergence in simultaneous approximation. This operator being capable of providing better approxima- tion than modified Baskakov operators.
基金NSF of China (11571089, 11871191) NSF of Hebei Province (2012205028+1 种基金 ZD2019053) Science foundation of Hebei Normal University
文摘The Meyer-König and Zeller operator is one of the most challenging operators. Sometimes the study of its properties will rely on the weighted approximation by Baskakov operator. In this paper, this relation is extended to complex space;the quantitative estimates and the Voronovskaja type results for analytic functions by complex Meyer-König and Zeller operators were obtained.
文摘In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
