The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropria...The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropriate weighted Lp-metric by the rate of Ditzian and Totik's r-th order weighted modulus of Smoothness.展开更多
In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type operators.We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global appro...In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type operators.We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of continuity.By means of construction of suitable functions and the method of Bojanic and Cheng,we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded variation function.展开更多
In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergenc...In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the q-Szasz-Beta operators, thus they improve the existing results.展开更多
In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to w...In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to wφ^24 （f, t）∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem.展开更多
In this paper, we investigate the simultaneous approximation of Bernstein- Sikkema operators, and establish the direct and equivalent theorems by using the Ditzian-Totik modulus of smoothness.
With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the...With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.展开更多
In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when ...In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.展开更多
In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we ob...In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.展开更多
Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.
文摘The author consides Beta operators βnf on suitable Sobolev type subspace of Lp[0, ∞) and characterizes the global rate of approximation of derivatives f(r) through corresponding derivatives (βnf)(r) in an appropriate weighted Lp-metric by the rate of Ditzian and Totik's r-th order weighted modulus of Smoothness.
基金This work is supported by the National Natural Science Foundation of China(11601266)the Natural Science Foundation of Fujian Province of China(2016J05017)the Program for New Century Excellent Talents in Fujian Province University and the Program for Outstanding Youth Scientific Research Talents in Fujian Province University.
文摘In this paper,we introduce the Bézier variant of two new families of generalized Bernstein type operators.We establish a direct approximation by means of the Ditzian-Totik modulus of smoothness and a global approximation theorem in terms of second order modulus of continuity.By means of construction of suitable functions and the method of Bojanic and Cheng,we give the rate of convergence for absolutely continuous functions having a derivative equivalent to a bounded variation function.
文摘In the present paper, we propose the q analogue of Szasz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained. Our results generalize and supplement some convergence results of the q-Szasz-Beta operators, thus they improve the existing results.
文摘In order to obtain much faster convergence, Miiller introduced the left Gamma quasi- interpolants and obtained an approximation equivalence theorem in terms of 2r wφ （f,t）p. Cuo extended the MiiUer＇s results to wφ^24 （f, t）∞. In this paper we improve the previous results and give a weighted approximation equivalence theorem.
基金the National Natural Science Foundation of China (10631080)the Zhejiang Provincial Key Basic Subject Foundation of China(10571014)
文摘In this paper, we investigate the simultaneous approximation of Bernstein- Sikkema operators, and establish the direct and equivalent theorems by using the Ditzian-Totik modulus of smoothness.
基金Supported by the 2007 Year School Grade Plan Item of Inner Mongolia University for Nationalities(MDX2007030)
文摘With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.
文摘In this paper, with the help of modulus of smoothness ω2r(f,t), we discuss the pointwise approximation properties for the iterated Boolean sums of Bernstein operator B n and obtain direct and inverse theorems when 1-1/r ≤λ≤ 1, r ∈N.
文摘In this paper, we use the equivalence relation between K-functional and modulus of smoothness, and give the Stechkin-Marchaud-type inequalities for linear combination of Bernstein-Durrmeyer operators . Moreover, we obtain the inverse result of approximation for linear combination of Bernstein-Durrmeyer operators with . Meanwhile we unify and extend some previous results.
基金Supported by the National Natural Science Foundation of China (1057104010801043)+1 种基金Natural Science Foundation of Hebei Province (08M001)Foundation of Education Department of Hebei Province (2008126)
文摘Bernstein-Kantorovich quasi-interpolants K^（2r-1）n（f, x） are considered and direct, inverse and equivalence theorems with Ditzian-Totik modulus of smoothness ω^2rφ（f, t）p （1 ≤ p ≤＋∞） are obtained.
基金Supported partially by the NSF(61877039)the NSFC/RGC Joint Research Scheme of China(12061160462 and N_CityU102/20)the NSF of Zhejiang Province(LY19F020013)。
