The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from ...The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.展开更多
The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong ...The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong uniqueness are established.展开更多
The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best app...The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's condition.Some recent results due to Lewicki and others are extended and improved.展开更多
In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended be...In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m^p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.展开更多
文摘The problem of strong uniqueness of best approximation from an RS set in a Banach space is considered. For a fixed RS set G and an element x∈X , we proved that the best approximation g * to x from G is strongly unique.
基金Supported in part by the National Natural Science Foundation of China(Grant No.10271025) 41A29,41A50
文摘The concept of an RS–set in a complex Banach space is introduced and theproblem of best approximation from an RS–set in a complex space is investigated. Results consistingof characterizations, uniqueness and strong uniqueness are established.
基金This work was supported in part by the National Natural Science foundations of China (Grant No 10271025).
文摘The present paper is concerned with problems of the strong uniqueness of the best approximation and the characterization of a uniqueness element in operator spaces.Some results on the strong uniqueness of the best approximation operatorfrom RS-sets are proved and the uniqueness element of a sun in the compactoperator space from c0 to c0 is characterized by the strict Kolmogorov's condition.Some recent results due to Lewicki and others are extended and improved.
基金supported by Consejo Nacional de Investigaciones Cientificas y Tecnicas(CONICET)and Universidad Nacional de San Luis(UNSL)with grants PIP(Grant No.11220110100033CO)PROICO(Grant No.30412)
文摘In this paper we pursue the study of the best approximation operator extended from L~Φ to L~φ, where φ denotes the derivative of the function Φ. We get pointwise convergence for the coefficients of the extended best approximation polynomials for a wide class of function f, closely related to the Calder′on–Zygmund class t_m^p(x) which had been introduced in 1961. We also obtain weak and strong type inequalities for a maximal operator related to the extended best polynomial approximation and a norm convergence result for the coefficients is derived. In most of these results, we have to consider Matuszewska–Orlicz indices for the function φ.
