Some Structures Related to Metric Projections in Orlicz Spaces

Bor-Luh Lin; Zhongrui Shi

Colloquium Mathematicae (1999)

  • Volume: 81, Issue: 2, page 223-235
  • ISSN: 0010-1354

Abstract

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We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.

How to cite

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Lin, Bor-Luh, and Shi, Zhongrui. "Some Structures Related to Metric Projections in Orlicz Spaces." Colloquium Mathematicae 81.2 (1999): 223-235. <http://eudml.org/doc/210736>.

@article{Lin1999,
abstract = {We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.},
author = {Lin, Bor-Luh, Shi, Zhongrui},
journal = {Colloquium Mathematicae},
keywords = {Orlicz function spaces; C-I property; C-III property; locally uniform convexity; Luxemburg norm; k-nearly uniform convexity; C-k-rotundity; nearly uniform convexity; weak k-rotundity; weak C-k-rotundity; k-β property; C-II property; k-rotundity; rotundity; nearly uniform convexity; property; locally uniform and nearly uniform convexity; Orlicz functions spaces},
language = {eng},
number = {2},
pages = {223-235},
title = {Some Structures Related to Metric Projections in Orlicz Spaces},
url = {http://eudml.org/doc/210736},
volume = {81},
year = {1999},
}

TY - JOUR
AU - Lin, Bor-Luh
AU - Shi, Zhongrui
TI - Some Structures Related to Metric Projections in Orlicz Spaces
JO - Colloquium Mathematicae
PY - 1999
VL - 81
IS - 2
SP - 223
EP - 235
AB - We discuss k-rotundity, weak k-rotundity, C-k-rotundity, weak C-k-rotundity, k-nearly uniform convexity, k-β property, C-I property, C-II property, C-III property and nearly uniform convexity both pointwise and global in Orlicz function spaces equipped with Luxemburg norm. Applications to continuity for the metric projection at a given point are given in Orlicz function spaces with Luxemburg norm.
LA - eng
KW - Orlicz function spaces; C-I property; C-III property; locally uniform convexity; Luxemburg norm; k-nearly uniform convexity; C-k-rotundity; nearly uniform convexity; weak k-rotundity; weak C-k-rotundity; k-β property; C-II property; k-rotundity; rotundity; nearly uniform convexity; property; locally uniform and nearly uniform convexity; Orlicz functions spaces
UR - http://eudml.org/doc/210736
ER -

References

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  13. [Na19] Na, Q. Y., On fully convex and locally fully convex Banach spaces, Acta Math. Sci. 10 (1990), 327-343. Zbl0734.46009
  14. [NaWa87] Nan, C. X., and Wang, J. H., Locally fully k-rotund and weakly locally fully k-rotund spaces, J. Nanjing Univ. Math. Biquarterly 2 (1989). 
  15. [NaWa871] Nan, C. X., Wang, J. H., On the Lk-UR and L-kR spaces, Math. Proc. Cambridge Philos. Soc. 104 (1988), 521-526. Zbl0673.46008
  16. [Pa83] Partington, J. R., On nearly uniformly convex Banach spaces, ibid. 93 (1983), 127-129. 
  17. [Wa95] Wang, J. H., Some results on the continuity of metric projections, Math. Appl. 8 (1995), 80-85. 
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