We present monotonicity theorems for index functions of N-fuctions, and obtain formulas for exact values of packing constants. In particular, we show that the Orlicz sequence space generated by the N-function N(v) = (1+|v|)ln(1+|v|) - |v| with Luxemburg norm has the Kottman constant , which answers M. M. Rao and Z. D. Ren’s [8] problem.
Let L [0, +∞) be the Orlicz function space generated by N-function Φ(u) with Luxemburg norm. We show the exact nonsquare constant of it when the right derivative φ(t) of Φ(u) is convex or concave.
Let Φ be an N-function, then the Jung constants of the Orlicz function spaces LΦ[0,1] generated by Φ equipped with the Luxemburg and Orlicz norms have the exact value: (i) If FΦ(t) = tφ(t)/Φ(t) is decreasing and 1 < CΦ < 2, then JC(L(Φ)[0,1]) = JC(LΦ[0,1]) = 21/CΦ-1; (ii) If FΦ...
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