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MR1105752 26E25 (46G99 46N10 49J27)
Averna, A.; Cardinali, T. On the concepts of $K$-convexity [$K$-concavity] and $K$-convexity$^*$ [$K$-concavity$^*$]. (Italian) Riv. Mat. Univ. Parma (4) 16 (1990), no. 1-2, 311–330 (1991).
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