Strongly unique minimization of functionals in Banach spaces with applications to theory of approximation and fixed points
type: Item
instance of: scholarly article
title: Strongly unique minimization of functionals in Banach spaces with applications to theory of approximation and fixed points
zbMATH Open document ID: 0593.49004
DOI: 10.1016/0022-247X(86)90030-2
published in: Journal of Mathematical Analysis and Applications
publication date: 1986-01-01T00:00:00Z
review text: The paper proves a theorem on the existence of a strong minimum point for a real valued functional defined on a closed convex set and fulfilling some growth conditions. A strong minimum for a functional means that every minimizing sequence converges to the minimum point (in other papers the property is called well-posedness, see e.g. \textit{T. Zolezzi} [Appl. Math. Optimization 4, 209-223 (1978; Zbl 0381.90105)]. Moreover, there are some estimates for the best approximation problem in Hilbert and \(L^ p\)-spaces and an existence theorem for (strongly unique) centers in a Banach space. The last result gets as a corollary an existence theorem of fixed points for a uniformly Lipschitz mapping on a Hilbert space.
Mathematics Subject Classification ID: 49J27
Mathematics Subject Classification ID: 41A50
Mathematics Subject Classification ID: 90C48
Mathematics Subject Classification ID: 46B99
Mathematics Subject Classification ID: 46C99
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 49K40
zbMATH DE Number: 3953658
zbMATH Keywords: strong minimum
zbMATH Keywords: well-posedness
zbMATH Keywords: best approximation problem
zbMATH Keywords: centers in a Banach space
zbMATH Keywords: existence theorem
zbMATH Keywords: fixed points
zbMATH Keywords: Hilbert space
author: Ryszard Smarzewski
reviewed by: Roberto Lucchetti
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3953658