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 a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev （and weakly-Chebyshev） subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.
The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonemp...The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.展开更多
This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the...This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.展开更多
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.
文摘Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
文摘In this paper, we shall introduce and characterize simultaneous quasi-Chebyshev （and weakly-Chebyshev） subspaces of normed spaces with respect to a bounded set S by using elements of the dual space.
基金the National Natural Science Foundation of China (Grant No. 19971013) and Natural Science Foundation of Jiangsu Province (Grant No. BK99001) .
文摘The well posedness of best simultaneous approximation problems is considered. We establish the generic results on the well posedness of the best simultaneous approximation problems for any closed weakly compact nonempty subset in a strictly convex Kadec Banach space. Further, we prove that the set of all points inE(G) such that the best simultaneous approximation problems are not well posed is a u- porous set inE(G) whenX is a uniformly convex Banach space. In addition, we also investigate the generic property of the ambiguous loci of the best simultaneous approximation.
基金Scientific Research Fund of Hunan Provincial Education Department (Grant No.06C651)the National Natural Science Foundation of China (Grant Nos.10671175,10731060)+1 种基金Program for New Century Excellent Talents in UniversityProjects MTM2006-13997-C02-01 and FQM-127 of Spain
文摘This paper is concerned with the problem of best weighted simultaneous approximations to totally bounded sequences in Banach spaces. Characterization results from convex sets in Banach spaces are established under the assumption that the Banach space is uniformly smooth.
