Abstract
Some relationships between compact full k-rotundity, compact local full k-rotundity and some other geometric properties in Banach spaces are discussed. It is also proved that in Orlicz function spaces equipped with the Orlicz norm, the notions of compact full k-rotundity and compact local full k-rotundity coincide. Moreover, it is shown that Orlicz spaces equipped with the Orlicz norm are compactly fully k-rotund if and only if they are reflexive and rotund.
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