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Let X be a Banach space and a continuous convex function on ΔK+1 satisfying certain conditions. Let (X⊕X⊕· · ·⊕X) ψ be the ψ-direct sum of X. In this paper, we characterize the K strict convexity, K uniform convexity and uniform non-lN 1 -ness of Banach spaces using ψ-direct sums. © 2013 The Korean Mathematical Society.

CHARACTERIZATIONS OF GEOMETRICAL PROPERTIES OF BANACH SPACES USING ψ-DIRECT SUMS