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Some Problems on Best Approximation in Orlicz Spaces  [PDF]
Garidi Wu, Dongyue Guan
Applied Mathematics (AM) , 2012, DOI: 10.4236/am.2012.34048
Abstract: 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.
Best approximation with wavelets in weighted Orlicz spaces  [PDF]
Maria de Natividade
Mathematics , 2009,
Abstract: Democracy functions of wavelet admissible bases are computed for weighted Orlicz Spaces in terms of its fundamental function. In particular, we prove that these bases are greedy if and only if the Orlicz space is a Lebesgue space. Also, sharp embeddings for the approximation spaces are given in terms of weighted discrete Lorentz spaces. For Lebesgue spaces the approximation spaces are identified with weighted Besov spaces.
Extension of the best approximation operator in Orlicz spaces and weak-type inequalities  [PDF]
Sergio Favier,Felipe Zò
Abstract and Applied Analysis , 2001, DOI: 10.1155/s1085337501000446
Abstract: We consider an extension of the best approximation operator froman Orlicz space L φto the space L φ′, where φ′denotes the derivative of φ, and we prove a weak-type inequality in this space. Further, we obtain some strong inequalities for suitable L ψ spaces.
The best simultaneous approximation in linear 2-normed spaces  [PDF]
Mehmet Acikgoz
Mathematics , 2012,
Abstract: In this paper, we shall investigate and analyse a new study on the best simultaneous approximation in the context of linear 2-normed spaces inspired by Elumalai and his coworkers in Elumalai. The basis of this investigation is to extend and refinement the definition of the classical aproximation, best approximation and some related concepts to linear 2-normed spaces.
Best approximation in Orlicz spaces  [cached]
H. Al-Minawi,S. Ayesh
International Journal of Mathematics and Mathematical Sciences , 1991, DOI: 10.1155/s0161171291000273
Abstract: Let X be a real Banach space and ( , ) be a finite measure space and be a strictly icreasing convex continuous function on [0, ¢ ) with (0)=0. The space L ( ,X) is the set of all measurable functions f with values in X such that ¢ ( ¢ € –c ¢ ’1f(t) ¢ € –)d (t)< ¢ for some c>0. One of the main results of this paper is: “For a closed subspace Y of X, L ( ,Y) is proximinal in L ( ,X) if and only if L1( ,Y) is proximinal in L1( ,X) ¢ € 2 ¢ € ¢ € 2. As a result if Y is reflexive subspace of X, then L ( ,Y) is proximinal in L ( ,X). Other results on proximinality of subspaces of L ( ,X) are proved.
New Characterization for Nonlinear Weighted Best Simultaneous Approximation  [PDF]
Xianfa Luo,Delin Wu,Jinsu He
International Journal of Mathematics and Mathematical Sciences , 2009, DOI: 10.1155/2009/194876
Abstract: This paper is concerned with the problem of a wide class of weighted best simultaneous approximation in normed linear spaces, and it establishes a new characterization result for the class of approximation by virtue of the notion of simultaneous regular point.
Extension of The Best Approximation Operator in Orlicz Spaces  [PDF]
Ivana Carrizo,Sergio Favier,Felipe Zó
Abstract and Applied Analysis , 2008, DOI: 10.1155/2008/374742
Approximative properties of diagonal operators in Orlicz spaces  [PDF]
Andriy L. Shidlich,Stanislav O. Chaichenko
Mathematics , 2014,
Abstract: We obtain the exact values of some important approximative quantities (such as, the best approximation, the basis width, Kolmogorov's width and the best $n$-term approximation) of certain sets of images of the diagonal operators in the Orlicz sequence spaces $l_M$.
Approximating Polynomials for Functions of Weighted Smirnov-Orlicz Spaces
Ramazan Akgün
Journal of Function Spaces and Applications , 2012, DOI: 10.1155/2012/982360
Abstract: Let 0 and ∞ be, respectively, bounded and unbounded components of a plane curve Γ satisfying Dini's smoothness condition. In addition to partial sum of Faber series of belonging to weighted Smirnov-Orlicz space , (0), we prove that interpolating polynomials and Poisson polynomials are near best approximant for . Also considering a weighted fractional moduli of smoothness, we obtain direct and converse theorems of trigonometric polynomial approximation in Orlicz spaces with Muckenhoupt weights. On the bases of these approximation theorems, we prove direct and converse theorems of approximation, respectively, by algebraic polynomials and rational functions in weighted Smirnov-Orlicz spaces ,(0) and ,(∞).
A result on best approximation in locally convex spaces
Abdul Latif,Arjamand Bano,Abdul Rahim Khan
Tamkang Journal of Mathematics , 2005, DOI: 10.5556/j.tkjm.36.2005.237-242
Abstract: In this paper we obtain a result on best approximation for multivalued nonexpansive maps in locally convex spaces. Our results generalize and extend some known results.
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