# Some Structures Related to Metric Projections in Orlicz Spaces

Colloquium Mathematicae (1999)

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

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topLin, 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

top- [An62] Ando, T., Weakly compact sets in Orlicz spaces, Canad. J. Math. 14 (1962), 170-196.
- [Ch86] Chen, S. T., Some rotundities in Orlicz spaces with Orlicz norm, Bull. Polish Acad. Sci. Math. 34 (1986), 585-596. Zbl0618.46031
- [Ch96] Chen, S. T., Geometry of Orlicz spaces, Dissertationes Math. 356 (1996).
- [ChWa92] Chen, S. T., and Wang, F. T., Uniformly rotund points of Orlicz spaces, J. Harbin Normal Univ. 8 (1992), no. 3, 5-10.
- [Hu83] Hudzik, H., Uniform convexity of Musielak-Orlicz spaces with Luxemburg norm, Comment. Math. (Prace Mat.) 23 (1983), 21-23.
- [HuLa95] Hudzik, H., and Landes, T., Packing constant in Orlicz spaces equipped with the Luxemburg norm, Boll. Un. Mat. Ital. A (7) 9 (1995), 225-237. Zbl0848.46017
- [Ka84] Kamińska, A., The criteria for local uniform rotundity of Orlicz spaces, Studia Math. 79 (1984), 201-215. Zbl0573.46014
- [Ku91] Kutzarova, D., k-β and k-nearly uniformly convex Banach spaces, J. Math. Anal. Appl. 162 (1991), 322-338. Zbl0757.46026
- [KuLi93] Kutzarova, D., Lin, B.-L., and Zhang, W. Y., Some geometrical properties of Banach spaces related to nearly uniform convexity, in: Banach Spaces (Merida, 1992), Contemp. Math. 144, Amer. Math. Soc., Providence, RI, 1993, 165-171. Zbl0804.46025
- [KuLi94] Kutzarova, D., and Lin, B.-L., Locally k-nearly uniformly convex Banach spaces, Math. Balkanica 8 (1994), 203-210. Zbl0896.46004
- [KrRu61] Krasnosel'skiĭ, M. A., and Rutitskiĭ, B. Ya., Convex Functions and Orlicz Spaces, Noordhoff, Groningen, 1961.
- [LiSh96] Lin, B.-L., and Shi, Z. R., On denting points and drop properties in Orlicz spaces, J. Math. Anal. Appl. 201 (1996), 252-273. Zbl0923.46020
- [Na19] Na, Q. Y., On fully convex and locally fully convex Banach spaces, Acta Math. Sci. 10 (1990), 327-343. Zbl0734.46009
- [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).
- [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
- [Pa83] Partington, J. R., On nearly uniformly convex Banach spaces, ibid. 93 (1983), 127-129.
- [Wa95] Wang, J. H., Some results on the continuity of metric projections, Math. Appl. 8 (1995), 80-85.
- [WaWa91] Wang, J. H., and Wang, M., Compact locally fully convex spaces, Ke Xue Tong Bao 36 (1991), 796.
- [Yu85] Yu, X. T., On LKUR spaces, Chinese Ann. of Math. Ser. B 6 (1985), 465-469.

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