Lower bounds for Jung constants of Orlicz sequence spaces

Z. D. Ren. "Lower bounds for Jung constants of Orlicz sequence spaces." Annales Polonici Mathematici 97.1 (2010): 23-34. <http://eudml.org/doc/280857>.

@article{Z2010,
abstract = {A new lower bound for the Jung constant $JC(l^\{(Φ)\})$ of the Orlicz sequence space $l^\{(Φ)\}$ defined by an N-function Φ is found. It is proved that if $l^\{(Φ)\}$ is reflexive and the function tΦ’(t)/Φ(t) is increasing on $(0,Φ^\{-1\}(1)]$, then $JC(l^\{(Φ)\}) ≥ (Φ^\{-1\}(1/2))/(Φ^\{-1\}(1))$. Examples in Section 3 show that the above estimate is better than in Zhang’s paper (2003) in some cases and that the results given in Yan’s paper (2004) are not accurate.},
author = {Z. D. Ren},
journal = {Annales Polonici Mathematici},
keywords = {Jung constant; Orlicz sequence space},
language = {eng},
number = {1},
pages = {23-34},
title = {Lower bounds for Jung constants of Orlicz sequence spaces},
url = {http://eudml.org/doc/280857},
volume = {97},
year = {2010},
}

TY - JOUR
AU - Z. D. Ren
TI - Lower bounds for Jung constants of Orlicz sequence spaces
JO - Annales Polonici Mathematici
PY - 2010
VL - 97
IS - 1
SP - 23
EP - 34
AB - A new lower bound for the Jung constant $JC(l^{(Φ)})$ of the Orlicz sequence space $l^{(Φ)}$ defined by an N-function Φ is found. It is proved that if $l^{(Φ)}$ is reflexive and the function tΦ’(t)/Φ(t) is increasing on $(0,Φ^{-1}(1)]$, then $JC(l^{(Φ)}) ≥ (Φ^{-1}(1/2))/(Φ^{-1}(1))$. Examples in Section 3 show that the above estimate is better than in Zhang’s paper (2003) in some cases and that the results given in Yan’s paper (2004) are not accurate.
LA - eng
KW - Jung constant; Orlicz sequence space
UR - http://eudml.org/doc/280857
ER -