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Streszczenie

A new lower bound for the Jung constant $JC(l^{({\mit\Phi})})$ of the Orlicz sequence space $l^{({\mit\Phi})}$ defined by an $N$-function ${\mit\Phi}$ is found. It is proved that if $l^{({\mit\Phi})}$ is reflexive and the function $t{\mit\Phi}'(t)/{\mit\Phi}(t)$ is increasing on $(0,{\mit\Phi}^{-1}(1)]$, then $$ JC(l^{({\mit\Phi})})\geq \frac{{\mit\Phi}^{-1}({1}/{2})}{{\mit\Phi}^{-1}(1)}. $$ 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.