We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the u...We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.展开更多
Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificati...Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.展开更多
In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting p...In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.展开更多
Boundary inner and outer operators are introduced, and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, co...Boundary inner and outer operators are introduced, and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.展开更多
To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy ap...To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.展开更多
We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M a...We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.展开更多
Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of th...Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.展开更多
In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compac...In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compact subset of real numbers. At the end of the paper the author applies this result for different classes of Q.展开更多
We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].
The best approximation, best Σ approximation and best sup approximation in linear 2 normed spaces are discussed in this paper. The characterization and uniqueness theorems for these nonlinear approximations are gi...The best approximation, best Σ approximation and best sup approximation in linear 2 normed spaces are discussed in this paper. The characterization and uniqueness theorems for these nonlinear approximations are given.展开更多
Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions...In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.展开更多
In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.
Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best...Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.展开更多
In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lore...In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.展开更多
In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonome...In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.展开更多
In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical correspo...In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical corresponding result.展开更多
This paper is part II of ＂On Copositive Approximation in Spaces of Contin- uous Functions＂. In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Che...This paper is part II of ＂On Copositive Approximation in Spaces of Contin- uous Functions＂. In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Chebyshev subspace of C （Q）, then for any admissible function f ∈ C（Q）／M, the best copositive approximation to f from M is unique.展开更多
We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (...We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the use of gradient information naturally. The algorithm is easy to implement, as it requires only vector operations and does not involve any matrices. We present tight error bound of the algorithm, and derive an optimal sampling probability measure that results in fastest error convergence. Numerical examples are provided to verify the theoretical error analysis and the effectiveness of the proposed SA algorithm.展开更多
In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ...In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ordered topological approximation spaces (GOTAS, for short). Some important properties of them were investigated. From this study, we can say that studying any properties of rough set concepts via GOTAS is a generalization of Pawlak approximation spaces and general approximation spaces.展开更多
文摘We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted Bergman,weighted Dirichlet,and weighted Besov spaces on the upper half-plane by dilatations and eventually by analytic polynomials.
文摘Recently,much interest has been given tomulti-granulation rough sets (MGRS), and various types ofMGRSmodelshave been developed from different viewpoints. In this paper, we introduce two techniques for the classificationof MGRS. Firstly, we generate multi-topologies from multi-relations defined in the universe. Hence, a novelapproximation space is established by leveraging the underlying topological structure. The characteristics of thenewly proposed approximation space are discussed.We introduce an algorithmfor the reduction ofmulti-relations.Secondly, a new approach for the classification ofMGRS based on neighborhood concepts is introduced. Finally, areal-life application from medical records is introduced via our approach to the classification of MGRS.
基金supported by the National Natural Science Foundation of China(12271344)the Natural Science Foundation of Shanghai(23ZR1425800)。
文摘In this paper,we study some dentabilities in Banach spaces which are closely related to the famous Radon-Nikodym property.We introduce the concepts of the weak^(*)-weak denting point and the weak^(*)-weak^(*)denting point of a set.These are the generalizations of the weak^(*)denting point of a set in a dual Banach space.By use of the weak^(*)-weak denting point,we characterize the very smooth space,the point of weak^(*)-weak continuity,and the extreme point of a unit ball in a dual Banach space.Meanwhile,we also characterize an approximatively weak compact Chebyshev set in dual Banach spaces.Moreover,we define the nearly weak dentability in Banach spaces,which is a generalization of near dentability.We prove the necessary and sufficient conditions of the reflexivity by nearly weak dentability.We also obtain that nearly weak dentability is equivalent to both the approximatively weak compactness of Banach spaces and the w-strong proximinality of every closed convex subset of Banach spaces.
基金Supported by the National Natural Science Foundation of China (No.69803007)
文摘Boundary inner and outer operators are introduced, and union, intersection, complement operators of approximations are redefined. The approximation operators have a good property of maintaining union, intersection, complement operators, so the rough set theory has been enriched from the operator-oriented and set-oriented views. Approximate power set spaces are defined, and it is proved that the approximation operators are epimorphisms from power set space to approximate power set spaces. Some basic properties of approximate power set space are got by epimorphisms in contrast to power set space.
基金supported by the Natural Science Foundation of Shandong Province (Y2006A12)the Scientific Research Development Project of Shandong Provincial Education Department (J06P01)+2 种基金the Science and Technology Foundation of Universityof Jinan (XKY0808 XKY0703)the Doctoral Foundation of University of Jinan (B0633).
文摘To study the problem of knowledge translation in fuzzy approximation spaces, the concept of rough communication of crisp set in fuzzy approximation spaces is proposed. In a rough communication of crisp set in fuzzy approximation spaces, the problem of uncertainty exists, for each agent has a different language and cannot provide precise communication to each other. By means of some concepts, such as CF rough communication cut, which is a bridge between fuzzy concept and crisp concept, cut analysis of CF rough communication is made, and the relation theorem between CF rough communication and rough communication of crisp concept is obtained. Finally, in order to give an intuitive analysis of the relation between CF rough communication and rough communication of crisp concept, an example is given.
文摘We assume that X is a normed linear space, W and M are subspaces of X. We develop a theory of best simultaneous approximation in quotient spaces and introduce equivalent assertions between the subspaces W and W ＋ M and the quotient space W/M.
基金supported by the National Science Foundation of China(No.11161033)Inner Mongolia Normal University Talent Project Foundation(No.RCPY-2-2012-K-036)
文摘Using the method of construction, with the help of inequalities, we research the Muntz rational approximation of two kinds of special function classes, and give the corresponding estimates of approximation rates of these classes under widely con- ditions. Because of the Orlicz Spaces is bigger than continuous function space and the Lp space, so the results of this paper has a certain expansion significance.
文摘In this paper the author writes a simple characterization for the best copositive approximation to elements of C(Q) by elements of finite dimensional strict Chebyshev subspaces of C(Q) in the case when Q is any compact subset of real numbers. At the end of the paper the author applies this result for different classes of Q.
文摘We prove some approximation properties of generalized Meyer-Konig and Zeller operators for differentiable functions in polynomial weighted spaces. The results extend some results proved in [1-3,7-16].
文摘The best approximation, best Σ approximation and best sup approximation in linear 2 normed spaces are discussed in this paper. The characterization and uniqueness theorems for these nonlinear approximations are given.
文摘Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.
文摘In this note we obtain generalization of well known results of carbone and Conti,Sehgal and Singh and Tanimoto concerning the existence of best approximation and simultaneous best approximation of continuous Junctions from the set up of a normed space to the case of a Hausdorff locally convex space.
文摘In this short note, we show the behavior in Orlicz spaces of best approximations by algebraic polynomials pairs on union of neighborhoods, when the measure of them tends to zero.
文摘Let (X,d) be a real metric linear space, with translation-invariant metric d and C a linear subspace of X. In this paper we use functionals in the Lipschitz dual of X to characterize those elements of G which are best approximations to elements of X.We also give simultaneous characterization of elements of best approximation and also consider elements of ε-approximation.
基金supported by the Ministry of Education and Science of Republic Kazakhstan(Grant No.5129/GF4)partially by the Russian Academic Excellence Project(agreement between the Ministry of Education and Science of the Russian Federation and Ural Federal University No.02.A03.21.006 of August 27,2013)
文摘In this paper, we consider a Lorentz space with a mixed norm of periodic functions of many variables. We obtain the exact estimation of the best M-term approximations of Nikol＇skii＇s and Besov＇s classes in the Lorentz space with the mixed norm.
文摘In this paper, Lorentz space of functions of several variables and Besov＇s class are considered. We establish an exact approximation order of Besov＇s class by partial sums of Fourier＇s series for multiple trigonometric system.
文摘In this paper we studied some problems on best approximation in Orlicz spaces, for which the approximating sets are Haar subspaces, the result of this paper can be considered as the extension of the classical corresponding result.
文摘This paper is part II of ＂On Copositive Approximation in Spaces of Contin- uous Functions＂. In this paper, the author shows that if Q is any compact subset of real numbers, and M is any finite dimensional strict Chebyshev subspace of C （Q）, then for any admissible function f ∈ C（Q）／M, the best copositive approximation to f from M is unique.
文摘We present an iterative algorithm for approximating an unknown function sequentially using random samples of the function values and gradients. This is an extension of the recently developed sequential approximation (SA) method, which approximates a target function using samples of function values only. The current paper extends the development of the SA methods to the Sobolev space and allows the use of gradient information naturally. The algorithm is easy to implement, as it requires only vector operations and does not involve any matrices. We present tight error bound of the algorithm, and derive an optimal sampling probability measure that results in fastest error convergence. Numerical examples are provided to verify the theoretical error analysis and the effectiveness of the proposed SA algorithm.
文摘In this paper, we introduce the concepts of g and b approximations via general ordered topological approximation spaces. Also, increasing (decreasing) g, b boundary, positive and negative regions are given in general ordered topological approximation spaces (GOTAS, for short). Some important properties of them were investigated. From this study, we can say that studying any properties of rough set concepts via GOTAS is a generalization of Pawlak approximation spaces and general approximation spaces.
