On the García-Falset coefficient in Orlicz sequence spaces equipped with the Orlicz norm (Q2712733)

Let \(X\) be a B-space, which does not have the Schur property, i.e. there exists a weakly convergent sequence in \(X\) which is not norm convergent. Also, let \(S(X)\) and \(B(X)\) denote the unit sphere and the unit ball of \(X\), respectively.NEWLINENEWLINENEWLINEIn his paper ``Stability and fixed points for nonexpansive mappings'' [Houston J. Math. 20, No. 3, 495-506 (1994; Zbl 0816.47062)] \textit{J. García-Falset} introduced the coefficient NEWLINE\[NEWLINER(X):= \sup\Biggl\{\liminf_n\|x_n- x\|:\{x_n\}\subset B(X), x_n@>w>> 0, x\in B(X)\Biggr\}NEWLINE\]NEWLINE in order to obtain the weak fixed-point property for some B-spaces. He proved that \(R(X)< 2\) is a sufficient condition for a B-space \(X\) to have the weak fixed-point property. The present authors obtain certain results determining the above coefficient for Orlicz sequence spaces equipped with the Orlicz norm.NEWLINENEWLINEFor the entire collection see [Zbl 0958.00028].