In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sid...In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.展开更多
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 problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability ...The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.展开更多
In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions dependin...In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.展开更多
Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several proble...In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.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
Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where J...Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2（[0, 1], x）, let E（f, n） be the error of the best L2（[0, 1], x）, i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T（t）f（x）=1/π∫0^π f（√x^2 ＋t^2-2xtcosO）dθ The differences （I- T（t））^r/2f = ∑j=0^∞（-1）^j（j^r/2）T^j（t）f of order r ∈ （0, ∞） and the L^2（[0, 1],x）- modulus of continuity ωr（f,τ） = sup{｜｜（I- T（t））^r/2f｜｜：0≤ t ≤τ] of order r are defined in the standard way, where T^0（t） = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E（f, n） and ωr（f, τ） for some cases of r and τ. More precisely, we will find the smallest constant n（τ, r） which depends only on n, r, and % such that the inequality E（f, n）≤ n（τ, r）ωr（f, τ） is valid.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 paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obta...In this paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obtained.展开更多
Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems an...Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.展开更多
In this paper, we introduce a condition weaker than the LP differentiability, which we call Cp condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation...In this paper, we introduce a condition weaker than the LP differentiability, which we call Cp condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation at that point. We also give a necessary and sufficient condition for that a function be LP differentiable. In addition, we study the convexity of the set of cluster points of the net of best appoximations of f, {Pε（f）} asε→0.展开更多
In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Ch...In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Chui et al. in 1984 are extensively used.展开更多
In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was intro...In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.展开更多
We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any ele...We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X展开更多
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 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.
In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1&...In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.展开更多
文摘In this paper, we continue studying the so called best m-term one-sided approximation and Greedy-liked one-sided ap- proximation by the trigonometric polynomials. The asymptotic estimations of the best m-terms one-sided approximation by the trigonometric polynomials on some classes of Besov spaces in the metricLp(Td(1≤p≤∞ are given.
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.
文摘The problem of best approximating, a given square complex matrix in the Frobenius norm by normal matrices under a given spectral restriction is considered. The ne cessary and sufficient condition for the solvability of the problem is given. A numerical algorithm for solving the problem is provided and a numerical example is presented.
基金This work is supported by Universidad Nacional de Rio Cuarto.
文摘In this paper we establish a result about uniformly equivalent norms and the convergence of best approximant pairs on the unitary ball for a family of weighted Luxemburg norms with normalized weight functions depending on ε, when ε→ 0. It is introduced a general concept of Pade approximant and we study its relation with the best local quasi-rational approximant. We characterize the limit of the error for polynomial approximation. We also obtain a new condition over a weight function in order to obtain inequalities in Lp norm, which play an important role in problems of weighted best local Lp approximation in several variables.
文摘Using reproducing kernels for Hilbert spaces, we give best approximation for Weierstrass transform associated with spherical mean operator. Also, estimates of extremal functions are checked.
基金Supported by Universidad Nacional de Rfo Cuaito and CONICET.
文摘In this paper we study best local quasi-rational approximation and best local approximation from finite dimensional subspaces of vectorial functions of several variables.Our approach extends and unifies several problems concerning best local multi-point approximation in different norms.
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 partly by National Natural Science Foundation of China (No.10471010)partly by the project"Representation Theory and Related Topics"of the"985 Program"of Beijing Normal University and Beijing Natural Science Foundation (1062004).
文摘Let L^2（[0, 1], x） be the space of the real valued, measurable, square summable functions on [0, 1] with weight x, and let n be the subspace of L2（[0, 1], x） defined by a linear combination of Jo（μkX）, where Jo is the Bessel function of order 0 and {μk} is the strictly increasing sequence of all positive zeros of Jo. For f ∈ L^2（[0, 1], x）, let E（f, n） be the error of the best L2（[0, 1], x）, i.e., approximation of f by elements of n. The shift operator off at point x ∈[0, 1] with step t ∈[0, 1] is defined by T（t）f（x）=1/π∫0^π f（√x^2 ＋t^2-2xtcosO）dθ The differences （I- T（t））^r/2f = ∑j=0^∞（-1）^j（j^r/2）T^j（t）f of order r ∈ （0, ∞） and the L^2（[0, 1],x）- modulus of continuity ωr（f,τ） = sup{｜｜（I- T（t））^r/2f｜｜：0≤ t ≤τ] of order r are defined in the standard way, where T^0（t） = I is the identity operator. In this paper, we establish the sharp Jackson inequality between E（f, n） and ωr（f, τ） for some cases of r and τ. More precisely, we will find the smallest constant n（τ, r） which depends only on n, r, and % such that the inequality E（f, n）≤ n（τ, r）ωr（f, τ） is valid.
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 paper, a new concept of weakly ,convex graph for set-valued mappings is introduced and studied. By using the concept , some new coincidence, the bestapproximation and fixed point-theorems are obtained.
文摘Some new coincidence theorem s involving a new class of set_valued mappings containing composites of acyclic mappings defined in a contractible space are proved. For applications, some best approximation theorems and coincidence theorems for set-valued mappings are als o given. A number of known results in recent literature are improved and general ized by the theorems in this paper.
基金supported by Universidad Nacional de Río Cuarto and Conicet
文摘In this paper, we introduce a condition weaker than the LP differentiability, which we call Cp condition. We prove that if a function satisfies this condition at a point, then there exists the best local approximation at that point. We also give a necessary and sufficient condition for that a function be LP differentiable. In addition, we study the convexity of the set of cluster points of the net of best appoximations of f, {Pε（f）} asε→0.
文摘In this survey the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, introduced by Chui et al. in 1984 are extensively used.
文摘In this survey, the notion of a balanced best multipoint local approximation is fully exposed since they were treated in the LP spaces and recent results in Orlicz spaces. The notion of balanced point, which was introduced by Chui et al. in 1984 are extensively used.
文摘We develop a theory of downward sets for a class of normed ordered spaces. We study best approximation in a normed ordered space X by elements of downward sets, and give necessary and sufficient conditions for any element of best approximation by a closed downward subset of X. We also characterize strictly downward subsets of X, and prove that a downward subset of X is strictly downward if and only if each its boundary point is Chebyshev. The results obtained are used for examination of some Chebyshev pairs （W,x）, where ∈ X and W is a closed downward subset of X
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.
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In numerical analysis, it is significant to approximate the linear functional Ef=sum from i=0 to m-1([integral from a to b(a<sub>1</sub>（x）f<sup>1</sup>（x）dx+ sum from f=0 to i<sub>1</sub>(b<sub>1</sub>f<sup>1</sup>（x<sub>1</sub>）)]) by a simpler linear functional Lf=sum from i=1 to m（a<sub>1</sub>f（x<sub>1</sub>）） In this paper, making use of natural Tchebysheff spline function, we give existence theorem and uniqueness theorem of L that is exact for the degree m to F; we also give three sufficient and necessary conditions in which L is the Sard best approximation to F.
