MEAN APPROXIMATION BY DILATATIONS IN BERGMAN SPACES ON THE UPPER HALF-PLANE

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.

Operators of Approximations and Approximate Power Set Spaces

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.

Rough communication of crisp concept in fuzzy approximation spaces

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.

Approximations by Ideal Minimal Structure with Chemical Application

The theory of rough set represents a non-statistical methodology for analyzing ambiguity and imprecise information.It can be characterized by two crisp sets,named the upper and lower approximations that are used to determine the boundary region and accurate measure of any subset.This article endeavors to achieve the best approximation and the highest accuracy degree by using the minimal structure approximation space MSAS via ideal J.The novel approach(indicated by JMSAS)modifies the approximation space to diminish the bound-ary region and enhance the measure of accuracy.The suggested method is more accurate than Pawlak’s and EL-Sharkasy techniques.Via illustrated examples,several remarkable results using these notions are obtained and some of their properties are established.Several sorts of near open(resp.closed)sets based on JMSAS are studied.Furthermore,the connections between these assorted kinds of near-open sets in JMSAS are deduced.The advantages and disadvan-tages of the proposed approach compared to previous ones are examined.An algorithm using MATLAB and a framework for decision-making problems are verified.Finally,the chemical application for the classification of amino acids(AAs)is treated to highlight the significance of applying the suggested approximation.

ON BEST SIMULTANEOUS APPROXIMATION IN QUOTIENT SPACES

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.

Muntz Rational Approximation for Special Function Classes in Orlicz Spaces

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.

On Copositive Approximation in Spaces of Continuous Functions I:The Alternation Property of Copositive Approximation

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.

APPROXIMATION BY GENERALIZED MKZ-OPERATORS IN POLYNOMIAL WEIGHTED SPACES

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].

Nonlinear Approximation in Linear 2 Normed Spaces

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.

FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES

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.

SOME BEST APPROXIMATION RESULTS IN LOCALLY CONVEX SPACES

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.

ON THE APPROXIMATION OF TCHEBYCHEFF-FOURIER SERIES IN THE C SPACE AND L_p~ω SPACE

The degree of approximation to a function f(x)∈C[-1,1] by (U, λ) means and f(x) ∈ Lpw by (Jr) means are discussed, some results in the literatures [1],[2],[3] have been improved.

A Note on Pad Approximants Pairs as Limits of Algebraic Polynomials Pairs of Weighted Best Approximation in Orlicz Spaces

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.

CHARACTERIZATION OF BEST APPROXIMATIONS IN METRIC LINEAR SPACES

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.

On M–Term Approximations of the Nikol'skii–Besov Class in the Lorentz Spaces

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.

On Approximation of Function Classes in Lorentz Spaces with Anisotropic Norm

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.

THREE KINDS OF DENTABILITIES IN BANACH SPACES AND THEIR APPLICATIONS

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.

Some Problems on Best Approximation in Orlicz Spaces

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.

On Copositive Approximation in Spaces of Continuous Functions Ⅱ:The Uniqueness of Best Copositive Approximation

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.

Sequential Approximation of Functions in Sobolev Spaces Using Random Samples

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.