An open problem of Alsina, Frank and Schweizer on k-Lipschitz t-norms is solved. k-convexity of monotone functions is introduced. Archimedean k-Lipschitz t-norms are shown to be generated by k-convex additive generators. Moreover, an example of a strict superadditive t-norm which is not a copula is given thus solving another open problem posed by Alsina, Frank and Schweizer.
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