WNUS property of Musielak-Orlicz sequence spaces

The coefficient R(X) is calculated for Orlicz sequence spaces equipped with the Luxemburg norm and for Cesaro spaces cesp(1p∞).An example of nonreflexive Banach space X with R(X)2 is given.It shows that property weak nearly uniformly smooth(WNUS) is essentially stronger than the inequality R(X)2.