In this paper, we prove that if X is a strictly convex Lk-UR space, then X is an L-kR space. However, the converse need not be true. Also, for each k ≥ 2, there exists a Lk-UR space which is URED but is not L-(k – 1)R.

In this paper we introduce and study the nearly uniformly norm upper semicontinuity for subdifferential mappings. Further we establish the interesting relations between uniform ␣ upper semicontinuity and nearly uniformly norm upper semi-Ž . continuity. Moreover, we discuss the weakly weak* uniformly upper semicontinuity and give applications in differentiability theory. ᮊ 1997 Academic Press

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