Using a recent result regarding the fixed points of multivalued mappings, the existence of invariant best simultaneous approximation in chainable metric space is proved.
Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on thei...Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.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Let the set of generalized polynomials having bounded coeffiicients be K={p=sum from j=1 to n α_j g_j α_j≤α_j≤β,j=1, 2,…, n}, where g_1, g_2,…, g_n are linearly independent continuous functions defined on theinterval [a,b], α_j β_j are extended real numbers satisfying α_j<+∞, β_j>? andα_j≤β_j. Assumethat f is a continuous function defined on a compact set X [a, b]. This paper gives the characterizationtheorem for p being the best uniform approximation to f from K, and points out that the characteri-zation theorem can be applied in calculating the approximate solution of best approximation to f fromK.
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.
