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
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 shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our app...In this paper, we shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our approach is a decompo- sition technique and a new type weights norm and flew K-function展开更多
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
In this paper, we derive the Baskakov-Kantorovich operators Vn（f; x） the complete asymptotic expansion in the form of all coefficients of n^-k, k =0, 1 … being calculated explicitly. As a corollary, we also get the...In this paper, we derive the Baskakov-Kantorovich operators Vn（f; x） the complete asymptotic expansion in the form of all coefficients of n^-k, k =0, 1 … being calculated explicitly. As a corollary, we also get the Voronovskaja-type result for the operators.展开更多
In the present paper, we deal with Chlodowsky type generalization of the Baskakov operators, special case of these operators includes Chlodowsky type Meyer–K?nig and Zeller operators(see [21]). With the help of Bohma...In the present paper, we deal with Chlodowsky type generalization of the Baskakov operators, special case of these operators includes Chlodowsky type Meyer–K?nig and Zeller operators(see [21]). With the help of Bohman-Korovkin theorem,we obtain some approximation properties for these operators. We give a modification of the operators in the space of differentiable functions and we also present examples of graphs for approximation. Finally, we apply these operators to the solution of the differential equation.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.
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 this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of ...In this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.展开更多
In this paper, we characterize the pointwise rate of convergence for the combinations of the Baskakov operators using the Ditzian-Totik modulus of smoothness.
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 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 [-1] Chen Wenzhong introduced the following generalized Baskakov oprators where a>0,f∈C[0,∞),b_(n,k,a)(X)= The purpose of this paper is to study the convergence,Voronovskaja-type asymptotic representations and...In [-1] Chen Wenzhong introduced the following generalized Baskakov oprators where a>0,f∈C[0,∞),b_(n,k,a)(X)= The purpose of this paper is to study the convergence,Voronovskaja-type asymptotic representations and the pointwise saturation of these operators. We shall give the direct and inverse theorems of weighted approximation and of uniform approximation.展开更多
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.
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.
文摘In this paper, we shall point out that the Multidimensional Baskakov opera- tors are unbounded in . Then we give a inverse theorems for multivariate Baskakov operators with Jacobi weights. A crucial tools in our approach is a decompo- sition technique and a new type weights norm and flew K-function
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.
基金Supported by the Natural Science Foundation of Beijing(1072006)Supported by NSFC(10871017)
文摘In this paper, we derive the Baskakov-Kantorovich operators Vn（f; x） the complete asymptotic expansion in the form of all coefficients of n^-k, k =0, 1 … being calculated explicitly. As a corollary, we also get the Voronovskaja-type result for the operators.
文摘In the present paper, we deal with Chlodowsky type generalization of the Baskakov operators, special case of these operators includes Chlodowsky type Meyer–K?nig and Zeller operators(see [21]). With the help of Bohman-Korovkin theorem,we obtain some approximation properties for these operators. We give a modification of the operators in the space of differentiable functions and we also present examples of graphs for approximation. Finally, we apply these operators to the solution of the differential equation.
文摘In this paper we establish direct local and global approximation theorems for Baskakov type operators and Szasz - Mirakjan type operators, respectively.
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Supported by the Scientific Research Fund of Zhejiang Province Education Depart-ment(200700190) Supported by the Science Technique Planed Item of Taizhou City(063KY08)Supported by Major Scientific Research Fund of Taizhou University(09ZD08)
文摘In this paper, we study the convergence rate of two-dimensional Baakakov operators with Jacobi-weights and the approximation equivalence theorem is obtained, making use of multivariate decompose skills and results of one-dimensional Baskakov operators.
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.
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 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].
文摘In [-1] Chen Wenzhong introduced the following generalized Baskakov oprators where a>0,f∈C[0,∞),b_(n,k,a)(X)= The purpose of this paper is to study the convergence,Voronovskaja-type asymptotic representations and the pointwise saturation of these operators. We shall give the direct and inverse theorems of weighted approximation and of uniform approximation.
