Strongly unique minimization of functionals in Banach spaces with applications to theory of approximation and fixed points

DOI10.1016/0022-247X(86)90030-2zbMath0593.49004MaRDI QIDQ1076327

Ryszard Smarzewski

Publication date: 1986

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

fixed pointsHilbert spacewell-posednessexistence theorembest approximation problemcenters in a Banach spacestrong minimum

Mathematics Subject Classification ID

Sensitivity, stability, well-posedness (49K40) Normed linear spaces and Banach spaces; Banach lattices (46B99) Fixed-point theorems (47H10) Best approximation, Chebyshev systems (41A50) Programming in abstract spaces (90C48) Existence theories for problems in abstract spaces (49J27) Inner product spaces and their generalizations, Hilbert spaces (46C99)

Related Items

Fixed point theorems for Lipschitzian semigroups in Banach spaces ⋮ On best approximation in \(L_ p\) spaces ⋮ Inequalities in Banach spaces with applications ⋮ Strongly unique best approximation in Banach spaces. II ⋮ Strong coapproximation in Banach spaces ⋮ Strongly unique best approximation in uniformly convex Banach spaces ⋮ Fixed point theorems for mappings with lipschitzian iterates ⋮ Local strong uniqueness ⋮ On some \(L^ p\) inequalities in best approximation theory ⋮ Resolvent flows for convex functionals and \(p\)-harmonic maps ⋮ Unnamed Item ⋮ On an inequality of Bynum and Drew ⋮ Fixed point theorems for uniformly Lipschitzian semigroups in uniformly convex spaces ⋮ Strong unicity of order 2 in C(T) ⋮ Strongly unique best approximations and centers in uniformly convex spaces ⋮ Strong uniqueness of the restricted Chebyshev center with respect to an RS-set in a Banach space

Cites Work

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• On the existence of best simultaneous approximation
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• Strongly unique best approximation in Banach spaces
• Best mean rational approximation
• Some theorems on Cebysev approximation
• Fixed point theorems for uniformly Lipschitzian mappings in LP spaces
• Sur le minimum des fonctionnelles dans les espaces de Banach
• On Asymptotic Centers and Fixed Points of Nonexpansive Mappings
• Fixed Point Theorems in Uniformly Convex Banach Spaces
• A fixed point theorem for transformations whose iterates have uniform Lipschitz constant
• Uniformly Convex Spaces
• Chebyshev centers in spaces of continuous functions

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