Best approximations, fixed points and parametric projections

Tiziana Cardinali

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2002)

  • Volume: 22, Issue: 2, page 243-260
  • ISSN: 1509-9407

Abstract

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If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].

How to cite

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Tiziana Cardinali. "Best approximations, fixed points and parametric projections." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 22.2 (2002): 243-260. <http://eudml.org/doc/271458>.

@article{TizianaCardinali2002,
abstract = {If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].},
author = {Tiziana Cardinali},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {fixed point; parametric projection; best approximation; upper semicontinuous; partially closed graph; f-approximatively compact; Oshman space},
language = {eng},
number = {2},
pages = {243-260},
title = {Best approximations, fixed points and parametric projections},
url = {http://eudml.org/doc/271458},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Tiziana Cardinali
TI - Best approximations, fixed points and parametric projections
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2002
VL - 22
IS - 2
SP - 243
EP - 260
AB - If f is a continuous seminorm, we prove two f-best approximation theorems for functions Φ not necessarily continuous as a consequence of our version of Glebov's fixed point theorem. Moreover, we obtain another fixed point theorem that improves a recent result of [4]. In the last section, we study continuity-type properties of set valued parametric projections and our results improve recent theorems due to Mabizela [11].
LA - eng
KW - fixed point; parametric projection; best approximation; upper semicontinuous; partially closed graph; f-approximatively compact; Oshman space
UR - http://eudml.org/doc/271458
ER -

References

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  3. [3] T. Cardinali and F. Papalini, Sull'esistenza di punti fissi per multifunzioni a grafo debolmente chiuso, Riv. Mat. Univ. Parma (4) 17 (1991), 59-67. 
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  11. [11] S. Mabizela, Upper semicontinuity of parametric projection, Set Valued Analysis 4 (1996), 315-325. Zbl0870.41022
  12. [12] T.D. Narang, On f-best approximation in topological spaces, Archivum Mathematicum, Brno 21 (4) (1985), 229-234. Zbl0585.41029
  13. [13] T.D. Narang, A note of f-best approximation in reflexive Banach space, Matem. Bech. 37 (1985), 411-413. Zbl0635.41031
  14. [14] E.V. Oshman, On the continuity of metric projection in Banach space, Math. USSR Sb. 9 (1969), 171-182. Zbl0198.45906
  15. [15] S. Reich, Approximate selections, best approximations, fixed points and invariant sets, J. Math. Anal. Appl. 62 (1978), 104-113. Zbl0375.47031
  16. [16] V.M. Seghal and S.P. Singh, A theorem on the minimization of a condensing multifunction and fixed points, J. Math. Anal. Appl. 107 (1985), 96-102. Zbl0602.47039
  17. [17] I. Singer, The theory of best approximation and functional analysis, Regional Conference Series in Applied Math., Philadelphia 1974. Zbl0291.41020
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  19. [19] E. Zeidler, Nonlinear Functional Analysis and its Applications II/A, Springer-Verlag 1990. Zbl0684.47028
  20. [20] E. Zeidler, Variational methods and optimization III, Springer-Verlag 1990. Zbl0684.47029

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